Perturbation Theory for the Solitary Wave Solutions to a Sasa-Satsuma Model Describing Nonlinear Internal Waves in a Continuously Stratified Fluid

摘要

The adiabatic evolution of perturbed solitary wave solutions to an extended Sasa-Satsuma (or vector-valued modified Korteweg-de Vries) model governing nonlinear internal gravity propagation in a continuously stratified fluid is considered. The transport equations describing the evolution of the solitary wave parameters are determined by a direct multiple-scale asymptotic expansion and independently by phase-averaged conservation relations for an arbitrary perturbation. As an example, the adiabatic evolution associated with a dissipative perturbation is explicitly determined. Unlike the case with the dissipatively perturbed modified Korteweg-de Vries equation, the adiabatic asymptotic expansion for the Sasa-Satsuma model considered here is not exponentially nonuniform and no shelf region emerges in the lee-side of the propagating solitary wave.