Slowly varying solitary waves. I  Kortewegde Vries equation. II  Nonlinear Schroedinger equation
Abstract
The paper constructs the slowly varying wave as an asymptotic solution of the variable coefficient Kortewegde Vries equation. A multiple scale method is used to determine the amplitude and phase of the wave to the second order in the perturbation parameter. In addition, the structure ahead and behind the solitary wave is also determined, and the results are interpreted by using conservation laws. Outer expansions are introduced to remove nonuniformities in the expansion. Finally, an exact solution is constructed when the coefficients satisfy a certain constraint.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 November 1979
 DOI:
 10.1098/rspa.1979.0135
 Bibcode:
 1979RSPSA.368..359G
 Keywords:

 Asymptotic Methods;
 KortewegDevries Equation;
 Perturbation Theory;
 Solitary Waves;
 Wave Dispersion;
 Boundary Value Problems;
 Conservation Laws;
 Independent Variables;
 Momentum Theory;
 Wave Equations;
 Physics (General)