Premium
Asymptotic Solution of the Weakly Nonlinear Schrödinger Equation with Variable Coefficients
Author(s) -
Srinivasan Radhakrishnan
Publication year - 1991
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1991842145
Subject(s) - mathematics , nonlinear system , mathematical analysis , fourier transform , nonlinear schrödinger equation , split step method , variable (mathematics) , perturbation (astronomy) , method of matched asymptotic expansions , asymptotic analysis , fourier analysis , asymptotic expansion , fourier series , schrödinger equation , physics , partial differential equation , differential equation , quantum mechanics
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.