Slowly varying solitary waves. II. Nonlinear Schrödinger equation
- 13 November 1979
- journal article
- Published by The Royal Society in Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
- Vol. 368 (1734) , 377-388
- https://doi.org/10.1098/rspa.1979.0136
Abstract
The slowly varying solitary wave is constructed as an asymptotic solution of the variable coefficient nonlinear Schrodinger equation. A multiple scale method is used to determine the amplitude and phases of the wave to the second order in the perturbation parameter. The method is similar to that used in (I) (R. Grimshaw 1979 Proc. R. Soc. Lond . A 368, 359). The results are interpreted by using conservation laws. Outer expansions are introduced to remove non-uniformities in the expansion. Finally, when the coefficients satisfy a certain constraint, an exact solution is constructed.Keywords
This publication has 1 reference indexed in Scilit:
- A general approach to linear and non-linear dispersive waves using a LagrangianJournal of Fluid Mechanics, 1965