Asymptotic Solution of the Weakly Nonlinear Schroedinger Equation with VariableCoefficients

摘要

A perturbation method based on Fourier analysis and multiple-scales is introducedfor solving weakly nonlinear, dispersive wave propagation problems with Fourier-transformable initial conditions. Asymptotic solutions are derived for the weakly nonlinear cubic Schrodinger 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 Schrodinger equation can be valid only for restricted initial conditions.