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On the asymptotic reduction to the multidimensional nonlinear Schrodinger equation

M. M. Shakir'yanov
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Abstract

The problem on the asymptotics for the solution of multidimensional nonlinear Boussinesq equation with respect to a small parameter $\ve$ is considered. The asymptotic expansion of the solution of this problem with respect to $\ve\to0$ for long times $t\sim {\cal O}(\ve^{-2})$ is constructed and justified. The leading terms of the asymptotic solution are defined from the multidimensional nonlinear Schrodinger equation and from the linear homogeneous wave equation.

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M. M. Shakir'yanov. 1999-07-02. On the asymptotic reduction to the multidimensional nonlinear Schrodinger equation. https://arxiv.org/abs/math-ph/9907003

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