 99363 Ricardo Weder
 Inverse Scattering for the Nonlinear Schroedinger Equation. Reconstruction of the Potential and the Nonlinearity.
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Sep 29, 99

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Abstract. In this paper we consider the inverse scattering problem for the nonlinear Schroedinger equation on the line:
$$ i \frac{\partial}{\partial t} u(t,x)= \frac{d^2}{dx^2} u(t,x)
+V_0(x) u(t,x) +\sum_{j=1}^{\infty} V_j(x) u^{2(j_0+j)} u(t,x).$$
We prove, under appropriate conditions, that the smallamplitude scattering operator determines uniquely, $V_j, j=0,1, \cdots $. Our proof gives also a method for the reconstruction of the $V_j, j=0,1,\cdots $.
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