Soliton solutions to coupled nonlinear evolution equations modelling a third harmonic resonance in the theory of capillary-gravity waves

摘要

Soliton solutions are sought to a pair of coupled nonlinear partial differential equations which model the interface of two stratified ideal fluids and which occur when a fundamental mode and its third harmonic component induce a resonant interaction. These equations bear a resemblance to the standard coupled nonlinear Schrodinger equations, but they contain additional terms which makes their analysis quite different. There are two parameters in the problem: the ratio of the velocity of the fluids and of their densities. A large number of solutions is found and some important special cases are studied in detail.