\font\tafont = cmbx10 scaled\magstep2 \font\tbfont = cmbx10 scaled\magstep1 \font\sixrm = cmr6 \font\petit = cmr8 \def\titlea#1#2{{~ \vskip 1 truecm \tafont Chapter {#1} - {#2} } \vskip 3truecm } \def\titleaa#1#2{{~ \vskip 1 truecm \tafont {#1} {#2} } \vskip 3truecm } \def\titleb#1#2{ \bigskip \bigskip {\tbfont {#1} {#2} } \bigskip} \def\fono{\footnote{}{{\sixrm G.Gaeta - "Geometrical symmetries of nonlinear equations and physics" - 1/3/93}}} \hfuzz=2pt \tolerance=500 \abovedisplayskip=2 mm plus6pt minus 4pt \belowdisplayskip=2 mm plus6pt minus 4pt \abovedisplayshortskip=0mm plus6pt minus 2pt \belowdisplayshortskip=2 mm plus4pt minus 4pt \predisplaypenalty=0 \clubpenalty=10000 \widowpenalty=10000 \parindent=0pt \parskip=10pt {\nopagenumbers \titleaa{A list of references concerning}{Lie-point symmetries of differential equations} \centerline{Giuseppe Gaeta} \centerline{Centre de Physique Theorique, Ecole Polytechnique} \centerline{F-91128 Palaiseau (France)} \medskip \centerline{gaeta@orphee.polytechnique.fr} \centerline{gaeta@roma1.infn.it} \vskip 3 truecm {\it What follows is the reference/bibliography section from a volume (maybe) in preparation; together with a few references concerned with other topics met in the course of the discussion along the volume, it gives a substantial amount of bibliography for what concerns Lie-point symmetries of differential equations, in particular for what concerns applications to equations of interest in Physics and Mathematical Physics; special attention is given to papers published in the last few years. I hope the work of collecting this bibliography can be of interest, and maybe even useful, to other people, so that I put it at disposition of anybody interested in the subject, in the hope I did not forget or overlook too many contributions; I would be glad of any help in filling the gaps in it.} \vfill \eject} \pageno=1 \def\JMP{{\it J. Math. Phys.}} \def\JPA{{\it J. Phys. A}} \def\PLA{{\it Phys. Lett. A}} \def\PRA{{\it Phys. Rev. A}} \def\PRL{{\it Phys. Rev. Lett.}} \def\RMS{{\it Russ. Math. Surv.}} \titleaa{}{References} \fono \font\petit = cmr9 {\petit For ease of the reader, we have collected here all the references quoted along the volume; we have also added a substantial number of other works which were not quoted but which deal directly or are concerned with, and/or relevant to, the general topic of Lie-point symmetries of differential equations. This bibliography has no ambition to be complete (and we apologize to authors which were not included only because of lack of attention by the present author), but we think it can be a service to the reader and help him to know about the existence and location of a certain amount of papers relevant to the topic; it seems to the author that this surely quite incomplete list is nevertheless the biggest one available at this moment. In the search for relevant papers, as the reader will easily notice, we have particularly concentrated our attention on recent contribution; this list can be supplemented with the works quoted in the bibliographic sections of Olver or Bluman and Kumei books. A number of older works are also quoted, too; in particular we have tried to quote a number of very old issues concerned with group analysis of differential equations we were aware of, to illustrate how the topic is not at all new, and how substantial steps were performed a long time ago (which does not exclude that they could have been forgotten for a while). The reader will also immediately notice that we have not quoted the father of all the story, i.e. Sophus Lie. The quotation of his complete works is, we think, implicit. Another, less easy to be fixed, hole in the bibliography is constituted by russian works which were not translated into western languages. Here no excuse is possible, and I can only apologize for not being able to acceed the russian literature, first of all for not reading russian. Some list of russian references can be find in the review papers (most of them appearing in {"Russian Mathematical Surveys"}) and books written by russian authors and quoted here. } \bigskip \bigskip \parskip=5pt \parindent=0pt \def\space{\vskip 10pt} {\tafont A} Abers and Lee; "Gauge theories", {\it Phys. Rep.} {\bf 9} (1973), 1 R. Abraham and J.E. Marsden, "Foundations of mechanics", Benjamin, New York, 1978 B. Abraham-Shrauner, "Lie transformation group solutions of the nonlinear one-dimensional Vlasov equation"; \JMP {\bf 26} (1985), 1428 B. Abraham-Shrauner, "Erratum : Lie transformation group solutions of the nonlinear one-dimensional Vlasov equation [J. Math. Phys. 26, 1428 (1985)]" \JMP {\bf 26} (1985), 3204 B. Abraham-Shrauner and A. Guo, "Hidden symmetries associated with the projective group of nonlinear first order ODEs"; \JPA {\bf 25} (1992), 5597 M. Abud and G. Sartori, "The geometry of spontaneous symmetry breaking"; {\it Ann. Phys.} {\bf 150} (1983), 307 M. Aguirre, C. Friedli and J. Krause, "SL(3,R) as the group of symmetry transformation for all one-dimensional linear systems. III. Equivalent Lagrangian formalism"; \JMP {\bf 33} (1992), 1571 M. Aguirre and J. Krause, "Infinitesimal symmetry transformations of some one-dimensional linear systems"; \JMP {\bf 25} (1984), 210 M. Aguirre and J. Krause, "Infinitesimal symmetry transformations. II. Some one-dimensional nonlinear systems"; \JMP {\bf 26} (1985), 593 M. Aguirre and J. Krause, "Some remarks on the Lie group of point transformations for the harmonic oscillator"; \JPA {\bf 20} (1987) 3553 M. Aguirre and J. Krause, "SL(3,R) as the group of symmetry transformations for all one-dimensional linear systems"; \JMP {\bf 29} (1988), 9 M. Aguirre and J. Krause, "SL(3,R) as the group of symmetry transformations for all one-dimensional linear systems. II. Realizations of the Lie algebra"; \JMP {\bf 29} (1988), 1746 M. Aguirre and J. Krause, "Finite point transformation and linearization of ${\ddot x}=f(t,x)$"; \JPA {\bf 21} (1988), 2841 M. Aguirre and J. Krause, "General transformation theory of Lagrangian mechanics and the Lagrangian group"; {\it Int. J. Theor. Phys.} {\bf 30} (1991), 495 M. Aguirre and J. Krause, "Point symmetry group of the Lagrangian"; {\it Int. J. Theor. Phys.} {\bf 30} (1991), 1461 M.A. Almeida and I.C. Moreira: "Lie symmetries for the reduced three-wave interaction problem"; \JPA {\bf 25} (1992), L669 A. Ambrosetti, V. Coti Zelati and I. Ekeland, "Symmetry breaking in hamiltonian systems", {\it J. Diff. Eqs.} {\bf 67} (1987), 165 W.F. Ames, J.E. Peters and M. Abell, "Symmetry and semi-symmetry reduction in wave propagation and lubrication"; in Hussin ed. 1990 W.F. Ames and C. Rogers eds., "Nonlinear equations in applied sciences"; Academic Press, New York, 1992 R. Anderson, S. Kumei and C.E. Wulfman, "Generalisation of the concept of invariance of differential equations". Results and applications to some Schroedinger equations"; \PRL {\bf 28} (1972), 988 S. Antman, ed., "Applications of bifurcation theory", Academic Press, New York (1977) D. Armbruster and P. Chossat, "Heteroclinic orbits in a spherically invariant system"; {\it Physica D} {\bf 50} (1991), 155 V.I. Arnold, "Equations differentielles ordinaires", M.I.R., Moscow 1974; "Equations Differentielles Ordinaires - IV edition", Mir, Moscow, 1990; "Ordinary Differential Equations - second edition", Springer Berlin, 1992 V.I. Arnold, "Les methodes mathematiques de la mecanique classique", M.I.R., Moscow 1976; "Mathematical Methods of Classical Mechanics"; Springer, Berlin, 1978; II ed., 1989 V.I. Arnold, "Chapitres supplementaires de la thorie des equations diffrentielles ordinaires", M.I.R., Moscow, 1980; "Geometrical Methods in the Theory of Ordinary Differential Equations"; Springer, Berlin, 1983 V.I. Arnold, "Bifurcation and singularities in mathematics and mechanics"; in, "Theoretical and applied mechanics, P. Germain et al. eds., North Holland 1989 V.I. Arnold; "Contact geometry and wave propagation"; Les Editions de L'Enseignement Mathematique (Geneva), 1990 V.I. Arnold, S.M. Gusein-Zade and A.N. Varchenko, "Singularities of differentiable mappings"; Birkhauser (Basel) 1985; "Singularites des applications differentiables"; MIR, Moscow, 1986 V.I. Arnold and S.P. Novikov eds.; "Dynamical Systems IV", Encyclopaedia of Mathematical Sciences, Springer (Berlin) 1990 E. Ascher and D. Gay, "Relative invariants of crystallographic point groups"; \JPA {\bf 18} (1985) 397 P.J. Aston, "Scaling laws and bifurcation"; in Roberts and Stewart 1991 P.J. Aston, "Analysis and computation of symmetry-breaking bifurcation and scaling laws using group theoretic methods"; {\it SIAM J. Math. Anal.} {\bf 22} (1991) 181 P.J. Aston, "Local and global aspects of the $(1,n)$ mode interaction for capillary- gravity waves"; {\it Physica D} {\bf 52} (1991), 415 P.J. Aston, A. Spence and W. Wu, "Bifurcation to rotating waves in equations with O(2)-symmetry"; preprint 1991, to appear in {\it SIAM J. Math. Anal.} C. Athorne, "On generalized Ermankov systems"; \PLA {\bf 159} (1991), 375 \space {\tafont B} K. Babu Joseph and B.V. Baby, "Classical SU(2) Yang-Mills-Higgs system : Time-dependent solutions by similarity method"; \JMP {\bf 26} (1985), 2746 V.A. Baikov, R.K. Gazizov and N.K. Ibragimov; {\it Math SSSR Sbornik} {\bf 64} (1989), 427 E. Barany, M. Golubitsky and J. Turski, "Bifurcations with local gauge symmetries in the Ginzburg- Landau equations"; {\it Physica D} {\bf 56} (1992), 36 A.O. Barut and A.J. Bracken, "Compact quantum systems: Internal geometry of relativistic systems"; \JMP {\bf 26}, 2515 (1985). A.O. Barut, A. Inomata and R. Wilson, "A new realization of dynamical group and factorization method"; \JPA {\bf 20} (1987), 4075 A.O. Barut, A. Inomata and R. Wilson, "Algebraic treatment of second Posch- Teller, Morse- Rosen and Eckart equations"; \JPA {\bf 20} (1987), 4083 G. Baumann and M. Freyberger, "Generalised symmetries and conserved quantities of teh Lotka- Volterra model"; \PLA {\bf 156} (1991), 488 G. Baumann, M. Freyberger, W.G. Glockle and T.F. Nonnenmacher, "Symilarity solutions in fragmentation kinetics"; \JPA {\bf 24} (1991), 5085 G. Baumann and T.F. Nonnenmacher, "Lie transformations, similarity reduction, and solutions for the nonlinear Madelung fluid equations with external potential"; \JMP {\bf 28} (1987), 1250 J. Beckers and N. Debergh, "On the Lie extended method in quantum physics and its supersymmetric version"; \JPA {\bf 23} (1990), L353 J. Beckers, N. Debergh and A.G. Nikitin, "More on the symmetries of the Schroedinger equation"; \JPA {\bf 24} (1991), L1269 J. Beckers, D. Dehin and V. Hussin, "Symmetries and supersymmetries of the quantum harmonic oscillator"; \JPA {\bf 20} (1987), 1137 J. Beckers, L. Gagnon, V. Hussin and P. Winternitz, "Superposition formulas for nonlinear superequations"; \JMP {\bf 31} (1990), 2528 J. Beckers, V. Hussin, and P. Winternitz, "Nonlinear equations with superposition formulas and the exceptional group $G(2)$. I. Complex and real forms of $g(2)$ and their maximal subalgebras"; \JMP {\bf 27} (1986), 2217 J. Beckers, V. Hussin, and P. Winternitz, "Nonlinear equations with superposition formulas and the exceptional group $ G(2)$. II. Classification of the equations"; \JMP {\bf 28}, 520 (1987) L.M. Berkovic and M.L. Nechaevsky, "On the group properties and integrability of the Fowler-Emden equations"; in M.A. Markov, V.I. Man'ko and A.E. Shabad 1985 J. Bertrand and G. Rideau, "Nonlinear representation of Poincar group in three dimensions"; \JMP {\bf 28}, 1972 (1987) E. Bierstone; {\it Topology} {\bf 14} (1975) E. Bierstone, "The structure of orbit spaces and the singularities of equivariant mappings", I.M.P.A., Rio de Janeiro (1980) M. Biesiada and M. Szydlowski, "On some group properties of structure equations of stellar systems"; \JPA {\bf 21} (1988), 3409 G. Birkhoff, "Dimensional analysis of partial differential equations"; {\it Electr. Eng.} {\bf 67} (1948), 1185 G. Birkhoff, "Hydrodynamics"; Princeton, 1960 G. Birkhoff and S. MacLane; "Elements of modern algebra", Macmillan (New York) 1941 G. Bluman, "Application of the general similarity solution of the heat equation to boundary-value problems"; {\it Quart. Appl. Math.} {\bf 31} (1974), 403 G. Bluman, "A reduction algorithm for an ordinary differential equation admitting a solvable Lie group"; {\it SIAM J. Appl. Math.} {\bf 50} (1990), 1689 G. Bluman, "Invariant solutions for ordinary differenial equations"; {\it SIAM J. Appl. Math.} {\bf 50} (1990), 1706 G. Bluman, "Potential symmetries"; in Hussin ed. 1990 G. Bluman, "Linearization of PDEs"; in Dodonov and Man'ko 1991 (p. 285) G.W. Bluman and J.D. Cole, "The general similarity solution of the heat equation"; {\it J. Math. Mech.} {\bf 18} (1969), 1025 G.W. Bluman and J.D. Cole, "Similarity methods for differential equations"; Springer (New York) 1974 G. Bluman and S. Kumei, "On invariance properties of the wave equation"; \JMP {\bf 28} (1987), 307 G. Bluman and S. Kumei," Exact solutions for wave equations of two-layered media with smooth transition"; \JMP {\bf 29}, 86 (1988) G.W. Bluman and S. Kumei, "Symmetries and differential equations"; Springer, New York, 1989 G.W. Bluman, G.J. Reid, and S. Kumei, "New classes of symmetries for partial differential equations"; \JMP {\bf 29} (1988), 806 G.W. Bluman, G.J. Reid, and S. Kumei, "Erratum : New classes of symmetries for partial differential equations [J. Math. Phys. 29, 806 (1988)]"; \JMP {\bf 29}, 2320 (1988) T.C. Bountis, V. Papageorgiou, and P. Winternitz, "On the integrability of systems of nonlinear ordinary differential equations with superposition principles"; \JMP {\bf 27} (1986), 1215 C.P. Boyer and J.F. Plebanski, "An infinite hierarchy of conservation laws and nonlinear superposition principles for self-dual Einstein spaces"; \JMP {\bf 26} (1985), 229 C.P. Boyer and P. Winternitz, "Symmetries of the self-dual Einstein equations. I. The infinite-dimensional symmetry group and its low-dimensional subgroups"; \JMP {\bf 30} (1989), 1081 G.E. Bredon, "Introduction to Compact Transformation Groups", Academic Press, New York, 1972 T.J. Bridges, "Hamiltonian bifurcation of the spatial structure for coupled nonlinear Schroedinger equations"; {\it Physica D} {\bf 57} (1992), 375 C.P. Bruter, ed., "Bifurcation theory, mechanics, and physics", Reidel, Dordrecht, 1983 F.H. Busse, "Pattern of convection in spherical shells"; {\it J. Fluid Mech.} {\bf 72} (1975), 65-85 F.H Busse and N. Riahi, "Pattern of convection in spherical shells, II"; {\it J. Fluid Mech.} {\bf 123} (1982), 283-291 E. Buzano and M. Golubitsky, "Bifurcation on the hexagonal lattice and the plane Benard problem"; {\it Phil. Trans. R. Soc. Lond.} {\bf A.308} (1983), 617-667 \vfill \eject \space {\tafont C} F. Cariello and M. Tabor, "Similarity reductions from extended Painlev\'e expansions for nonintegrable evolution equations"; {\it Physica D} {\bf 53} (1991), 59 J.F. Carinema, M.A. del Olmo and M. Santander, "A new look at dimensional analysis from a group theoretical viewpoint"; \JPA {\bf 18} (1985), 1855 J.F. Carinena, M. A. Del Olmo, and M. Santander, "Locally operating realizations of transformation Lie groups"; \JMP {\bf 26} (1985), 2096 J.F. Carinema, M.A. Del Olmo and P. Winternitz, "Cohomology and symmetry of differential equations"; in Dodonov and Man'ko 1991 (p. 272) J.F. Carinena, C. Lopez and E. Martinez, "A new approach to the converse of Noether's theorem"; \JPA {\bf 22} (1989), 4777 J.F. Carinena and E. Martinez, "Symmetry theory and Lagrangian inverse problem for time-dependent second order differential equations"; \JPA {\bf 22} (1989), 2659 J. Carr, "Applications of Centre Manifold Theory", Springer, New York, 1981 J.A. Cavalcante and K. Tenenblat, "Conservation laws for nonlinear evolution equations"; \JMP {\bf 29} (1988), 1044 G. Caviglia, "Composite variational principles and the determination of conservation laws"; \JMP {\bf 29} (1988), 812 G. Caviglia and A. Morro, "Noether-type conservation laws for perfect fluid motions"; \JMP {\bf 28} (1987), 1056 J.M. Cervero and J. Villarroel, "Contact symmetries and integrable non- linear dynamical systems"; \JPA {\bf 20} (1987), 6203 B. Champagne and P. Winternitz, "On the infinite-dimensional symmetry group of the Davey-Stewartson equations"; \JMP {\bf 29} (1988), 1 B. Champagne, W. Hereman and P. Winternitz, "The computer calculation of Lie point symmetries of large systems of differential equations"; {\it Comp. Phys. Comm.} {\bf 66} (1991), 319 D.R.J. Chillingworth, J.E. Marsden and Y.H. Wan, "Symmetry and bifurcation in the three-dimensional elasticity"; {\it Arch. Rat. Mech. Anal.} {\bf 80} (1982), 295 D.R.J. Chillingworth, J.E. Marsden and Y.H. Wan, "Symmetry and bifurcation in the three-dimensional elasticity II"; {\it Arch. Rat. Mech. Anal.} {\bf 83} (1982), 363 P. Chossat, "Bifurcation and stability of convective flows in rotating or not rotating spherical shell"; {\it S.I.A.M. J. Appl. Math.} {\bf 37} (1979), 624 P. Chossat and M. Golubitsky, "Hopf bifurcation in the presence of symmetry, center manifold and Liapunov-Schmidt reduction", in Atkinson et. al. (1987), 343 P. Chossat and M. Golubitsky, "Iterates of maps with symmetry"; {\it SIAM J. Math. Anal.} {\bf 19} (1988), 1259 S.N. Chow and J. Hale, "Methods of Bifurcation Theory", Springer, New York, (1982) G. Cicogna, "Symmetry breakdown from bifurcation"; {\it Lett. Nuovo Cimento} {\bf 31} (1981), 600 G. Cicogna, "A nonlinear version of the equivariant bifurcation lemma"; \JPA {\bf 23} (1990), L1339 G. Cicogna and G. Gaeta, "Periodic solutions from quaternionic bifurcation"; {\it Lett. Nuovo Cimento} {\bf 44} (1985), 65 G. Cicogna and G. Gaeta, "Spontaneous linearization and periodic solutions in Hopf and symmetric bifurcations"; {\it Phys. Lett. A} {\bf 116} (1986), 303 G. Cicogna and G. Gaeta, "Quaternionic bifurcation and SU(2) symmetry"; Preprint Pisa-IFU (1986) G. Cicogna and G. Gaeta, "Hopf - type bifurcation in the presence of multiple critical eigenvalues"; \JPA {\bf 20} (1987), L425 G. Cicogna and G. Gaeta, "Quaternionic-like bifurcation in the absence of symmetry"; \JPA {\bf 20} (1987), 79 G. Cicogna and G. Gaeta, "Lie-point symmetries and Poincare' normal forms for dynamical systems"; \JPA {\bf 23} (1990), L799 G. Cicogna and G. Gaeta, "Lie-point symmetries for autonomous systems and resonance"; \JPA {\bf 25} (1992), 1535 G. Cicogna and G. Gaeta, "Lie-point symmetries in bifurcation problems"; {\it Ann. Inst. H. Poincare'} {\bf 56} (1992), 375 G. Cicogna and G. Gaeta, "Lie-point symmetries in Mechanics"; {\it Nuovo Cimento} {\bf B 107} (1992), 1085 G. Cicogna and G. Gaeta, "Nonlinear symmetries in bifurcation theory"; \PLA (1993) G. Cicogna and D. Vitali, "Generalised symmetries of Fokker-Planck - type equations"; {\it J. Phys. A} {\bf 22} (1989), L453 G. Cicogna and D. Vitali, "Classification of the extended symmetries of Fokker-Planck equations"; {\it J. Phys. A} {\bf 23} (1990), L85 P.A. Clarkson, "New similarity solutions for the modified Boussinesq equation"; \JPA {\bf 22} (1989), 2355 P.A. Clarkson, "New similarity reduction and Painleve' analysis for the symmetric regularised long wave and modified Benjamin-Bona-Mahoney equations"; \JPA {\bf 22} (1989), 3821 P.A. Clarkson, "Nonclassical symmetry reduction and exact solutions for physically significant nonlinear evolution equations"; in Rozmus and Tuszynski eds., 1991 P.A. Clarkson and S. Hood, "Symmetry reductions of a generalized, cylindrical Schroedinger equation"; \JPA {\bf 26} (1993), 133 P.A. Clarkson and M.D. Kruskal, "New similarity reduction of the Boussinesq equation"; \JMP {\bf 30} (1989), 2201 P.A. Clarkson and J.A. Tuszynski, "Exact solutions of the multidimensional derivative nonlinear Schroedinger equation for many-body systems near criticality"; \JPA {\bf 23} (1990), 4269 P.A. Clarkson and P. Winternitz, "Nonclassical symmetry reduction for the Kadomtsev- Petviashvili equation"; {\it Physica D} {\bf 49} (1991), 257 E.A. Coddington and N. Levinson, "Theory of ordinary differential equations", Mc Graw - Hill, London, 1955 S.V. Coggeshall and J. Meyer-ter-Vehn, "Group-invariant solutions and optiml systems for multidimensional hydrodynamics"; \JMP {\bf 33} (1992), 3585 A. Cohen, "An introduction to the Lie theory of one-parameter groups with applications to the solution of differential equations"; Boston 1911 J. Cole, "Scale factors and similarity solutions"; in Hussin ed. 1990 P. Collet and J.P. Eckmann, "Instabilities and fronts in extended systems", Princeton University Press, 1990 R. Courant and D. Hilbert, "Methods of Mathematical Physics"; Wiley M. Crandall and P. Rabinowitz, "Bifurcation from simple eigenvalues"; {\it J. Func. Anal.} {\bf 8} (1971), 321 M. Crandall and P. Rabinowitz, "Bifurcation, perturbation of simple eigenvalues, and linearized stability"; {\it Arch. Rat. Mech. Anal.} {\bf 52} (1973), 161 M. Crandall and P. Rabinowitz, "The Hopf bifurcation theorem in infinite dimensions"; {\it Arch. Rat. Mech. Anal.} {\bf 67} (1977), 53 J.D. Crawford, "Surface waves in nonsquare containers with square symmetry"; {\it Phys. Rev. Lett.} {\bf 67} (1991), 441 J.D. Crawford, "Introduction to Bifurcation Theory"; {\it Rev. Mod. Phys.} (1991) J.D. Crawford, "Normal forms for driven surface waves: boundary conditions, symmetry, and genericity"; {\it Physica D} {\bf 52} (1991), 429 J.D. Crawford, M. Golubitsky, M.G.M. Gomes, E. Knobloch and I. Stewart, "Boundary conditions as symmetry constraints"; in "Singularity Theory and its Applications, Warwick 1989", R.M. Roberts and I. Stewart eds., Lecture Notes in Mathematics, Springer, Berlin, 1991 J.D. Crawford and E. Knobloch, "Symmetry breaking bifurcations in O(2) maps"; \PLA {\bf 128}, 327 J.D. Crawford and E. Knobloch, "On degenerate Hopf bifurcation with O(2) symmetry"; {\it Nonlinearity} {\bf 1} (1988), 617 J.D. Crawford and E. Knobloch, "Symmetry and symmetry-breaking bifurcations in fluid dynamics"; {\it Ann. Rev. Fluid Mech.} {\bf 23} (1991), 341 \space {\tafont D} E.N. Dancer, "On the existence of bifurcating solutions in the presence of symmetries"; {\it Proc. Roy. Soc. Edin.} {\bf 85A} (1980), 321 E.N. Dancer, "An implicit function theorem with symmetries and its application to nonlinear eigenvalues problems"; {\it Bull. Austral. Math. Soc.} {\bf 21} (1980), 404 E.N. Dancer, "The G-invariant implicit function theorem in infinite dimensions"; {\it Proc. Roy. Soc. Edin.} {\bf 92A} (1982), 13 E.N. Dancer, "Bifurcation under continuous groups of symmetry"; in "Systems of Nonlinear Partial Differential Equations", J.M. Ball Ed. Reidel, (1983), 343 E.N. Dancer, "The G-invariant implicit function theorem in infinite dimensions Part II"; {\it Proc. Roy. Soc. Edin.} {\bf 102A} (1986), 211 Daniel and Viallet; "The geometrical setting of gauge theories of Yang-Mills type"; {\it Rev. Mod. Phys.} {\bf 52} (1980), 175 Y.A. Danilov and G.I. Kuznetsov, "Nonlinear equations and differential invariants"; in M.A. Markov, V.I. Man'ko and A.E. Shabad 1985 G. Dattoli, M. Richetta, G. Schettini and A. Torre, "Lie algebraic methods and solutions of linear partial differential equations"; \JMP {\bf 31} (1990), 2856 D. David, "Symmetry reduction for the KP equation and its Backlund transformation"; in Gilmore 1987 (p. 451) D. David, N. Kamran, D. Levi, and P. Winternitz, "Symmetry reduction for the Kadomtsev-Petviashvili equation using a loop algebra"; \JMP {\bf 27} (1986), 1225 D. David, D. Levi and P. Winternitz, "Backlund transformations and the infinite-dimensional symmetry group of the Kadomtsev- Petviashvili equation"; \PLA {\bf 118} (1986), 390 D. David, D. Levi and P. Winternitz, "Equations invariant under the symmetry group of the Kadomtsev- Petviashvili equation"; \PLA {\bf 129} (1988), 161 G.F. Dell'Antonio and B.M. D'Onofrio, eds., "Recent advances in Hamiltonian systems"; World Scientific, 1987 M.A. Del Olmo, M.A. Rodriguez and P. Winternitz, "Simple subgroups of simple Lie groups and nonlinear differential equations with superposition principles"; \JMP {\bf 27} (1986), 14 M. Del Olmo, M.A. Rodriguez and P. Winternitz, "Superposition formulas for rectangular matrix Riccati equations"; \JMP {\bf 28} (1987), 530 G. Denardo, G. Ghirardi and T. Weber, eds., "Group theoretical methods in Physics", proceedings of the XII ICGTMP; {\it Lecture Notes in Physics} 201, Springer, Berlin, 1984 C. Deng- yuan, D. Levi and L. Yi- shen, "Equivalent classes of integrable non linear evolution equations and generalised Miura transformation"; \JPA {\bf 20} (1987), 313 L.E. Dickson, "Differential equations from the group standpoint"; {\it Ann. Math.} {\bf 25} (1924), 287 R. Dirl and M. Moshinsky, "Accidental degeneracy and symmetry Lie algebra"; \JPA {\bf 18} (1985) 2423 J.M. Dixon, M. Kelley and J.A. Tuszynski, "Coherent structures from the three- dimensional nonlinear Schroedinger equation"; \PLA {\bf 170} (1992), 77 J.M. Dixon and J.A. Tuszynski, "Solutions of a generalized Emden equation and their physical significance"; {\it Phys. Rev. A} {\bf 41} (1990), 4166 V.V. Dodonov and V.I. Man'ko, eds., "Group theoretical methods in physics" (Proceedings of the XVIII ICGTMP, Moscow 1990), Lect. Notes Phys. 382, Springer, Berlin, 1991 A. Doelman, "On the nonlinear evolution of patterns"; Ph.D. thesis, Utrecht, 1990 B. Dorizzi, B. Grammaticos, A. Ramani, and P. Winternitz, "Are all the equations of the Kadomtsev-Petviashvili hierarchy integrable?" \JMP {\bf 27} (1986), 2848 B. Dorizzi, B. Grammaticos, A. Ramani, and P. Winternitz, "Integrable Hamiltonian systems with velocity-dependent potentials"; \JMP {\bf 26} (1985), 3070 L.G.S. Duarte, S.E.S. Duarte and I.C. Moreira, "One dimensional equations with the maximum number of symmetry generators"; \JPA {\bf 20} (1987), L701 L.G.S. Duarte, S.E.S. Duarte and I.C. Moreira, "N-dimensional equations with the maximum number of symmetry generators"; \JPA {\bf 22} (1989), L201 B. Dubrovin, S.P. Novikov and A. Fomenko, "Modern Geometry I \& II", Springer 1984; "Geometrie Contemporaine I, II \& III", Mir, Moscow, 1982 \& 1987 \space {\tafont E} J.P. Eckmann, G. Goren and I. Procaccia, "Nonequilibrium nucleation of topological defects as a deterministic phenomenon"; {\it Phys. Rev. Lett.} {\bf 44} (1991), R805 T. Eguchi, P.B. Gilkey and A.J. Hanson, "Gravitation, gauge theories, and differential geometry"; {\it Phys. Rep.} {\bf 66} (1980), 213 C. Ehresmann, "Les prolongements d'une variete' differentiable", I-V; {\it C. R. Acad. Sci. Paris}, "I. Calcul des jets, prolongement principal" {\bf 233} (1951), 598; "II. L'espace des jets d'ordre $r$ de $V_n$ dans $V_m$" {\bf 233} (1951), 777; "III. Transitivite' des prolongements" {\bf 233} (1951), 1081; "IV. Elements de contact et elements d'enveloppe" {\bf 234} (1952), 1028; "V. Covariants differentiels et prolongements d'une structure infinitesimale" {\bf 234} (1952), 1424. "Structures locales et structures infinitesimales", {\bf 234} (1952), 587; "Extension du calcul des jets aux jets non holonomes", {\bf 239} (1954), 1762; "Applications de la notion de jet non holonome", {\bf 240} (1955), 397; "Les prolongements d'un espace fibre' differentiable", {\bf 240} (1955), 1755. "Les prolongements d'une variete' differentiable"; {\it Atti del IV congresso dell'Unione Matematica Italiana} (1951) C. Elphick, "Classes of exactly solvable nonlinear evolution equations for Grassmann variables: The normal form method"; \JMP {\bf 28} (1987), 1243 C. Elphick, E. Tirapegui, M.E. Brachet, P. Coullet and G. Iooss, "A simple global characterization for normal forms of singular vector fields"; {\it Physica D} {\bf 29} (1987), 95 N. Euler, M.W. Shul'ga and W.H. 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Sinzinkayo, "Conformal symmetry and constants of motion"; \JMP {\bf 26} (1985), 1072 \space {\tafont I} N.H. Ibragimov and M. Torrisi, "A simple method for group analysis and its application to a model of detonation"; \JMP {\bf 33} (1992), 3931 N.H. Ibragimov, M. Torrisi and A. Valenti, "Preliminary group classification of equations $v_{tt} = f(x,v_x ) v_{xx} + g(v,v_x )$"; \JMP {\bf 32} (1991), 2988 E. Ihrig and M. Golubitsky, "Pattern selection with O(3) symmetry"; {\it Physica D}, {\bf 12} (1984), 1 G. Iooss, "Bifurcation of maps and applications"; North Holland, Amsterdam, 1979 G. Ioos and D.D. Joseph, "Elementary stability and bifurcation theory"; Springer, Berlin, 1981; second edition 1990 T.Iwai and Y. Uwano, "The quantized MIC-Kepler problem and its symmetry group for negative energies"; \JPA {\bf 21} (1988), 4083 \space {\tafont J} M. Jaric, L. Michel and R. 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Mahomed, "Maximal subalgebra associated with a first integral of a system possessing $SL(3,R)$ algebra"; \JMP {\bf 29} (1988), 1807 Y.Q. Lee and J.F. Lu, "Prolongation structure and infinite dimensional algebra for the isotropic Landau-Lifsits equation"; \PLA {\bf 135} (1989), 117 M. Legar\'e, "Supersymmetry representations from symmetry reductions of the Wess-Zumino model"; in Hussin ed., 1990 R.A. Leo, L. Martina, and G. Soliani, "Group analysis of the three-wave resonant system in (2+1) dimensions"; \JMP {\bf 27} (1986), 2623 D. Levi, "Integrable systems and water waves. An example of symmetry analysis applied to a physical problem"; in Levi and Winternitz eds. 1988 (p. 121) D. Levi, C.R. Menyuk and P. Winternitz, "Exact solutions of the stimulated Raman scattering equations"; {\it Phys. Rev. A} {\bf 44} (1991), 6057 D .Levi, M.C. Nucci, C. Rogers and P. Winternitz, "Group theoretical analysis of a rotating shallow liquid in a rigid container; \JPA {\bf 22} (1989), 4743 D. 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