99-363 Ricardo Weder
Inverse Scattering for the Nonlinear Schroedinger Equation. Reconstruction of the Potential and the Nonlinearity. (32K, Latex) 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 small-amplitude 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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