 0083 Paleari, S., Bambusi, D., Cacciatori, S.
 Exponential stability in a nonlinear string equation
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Feb 23, 00

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Abstract. We study the nonlinear wave equation
$u_{tt}c^2u_{xx}=\psi(u) \qquad u(0,t)=0=u(\pi,t)$
with an analytic nonlinearity of the type $\psi(u)=\pm u^3 +
\sum_{k\ge 4}\alpha_k u^k$. On each smallenergy surface we consider
a solution of the linearized system with initial datum having the
profile of an elliptic sinus: we show that solutions starting close to
the corresponding phase space trajectory remain close to it for times
growing exponentially with the inverse of the energy. To obtain the
result we have to compute the resonant normal form of \ref{equa}, and
we think this could be interesting in itself.
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