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Asymptotic Solution of the Weakly Nonlinear Schrödinger Equation with Variable Coefficients

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A perturbation method based on Fourier analysis and multiple scales is introduced for solving weakly nonlinear, dispersive wave propagation problems with Fourier‐transformable initial conditions. Asymptotic solutions are derived for the weakly nonlinear cubic Schrödinger equation with variable coefficients, and verified by comparison with numerical solutions. In the special case of constant coefficients, the asymptotic solution agrees to leading order with previously derived results in the literature; in general, this is not true to higher orders. Therefore previous asymptotic results for the strongly nonlinear Schrödinger equation can be valid only for restricted initial conditions.
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Document Type: Research Article

Affiliations: National Aeronautical Laboratory, India

Publication date: February 1, 1991

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