Well-posedness for multicomponent Schrodinger-gKdV systems and stability of solitary waves with prescribed mass

TL;DR

This paper establishes well-posedness, existence of solutions with prescribed mass, and stability of solitary waves for coupled Schrödinger-gKdV systems, extending previous results to more complex multicomponent dispersive equations.

Contribution

It introduces new results on well-posedness, solution existence, and stability for two classes of coupled nonlinear dispersive equations involving Schrödinger and gKdV components.

Findings

Proved well-posedness of initial value problems for the systems.

Established existence of solutions with prescribed $L^2$-norm.

Demonstrated stability of solitary waves in the systems.

Abstract

In this paper we prove the well-posedness issues of the associated initial value problem, the existence of nontrivial solutions with prescribed $L^2$-norm, and the stability of associated solitary waves for two classes of coupled nonlinear dispersive equations. The first problem here describes the nonlinear interaction between two Schr\"{o}dinger type short waves and a generalized Korteweg-de Vries type long wave and the second problem describes the nonlinear interaction of two generalized Korteweg-de Vries type long waves with a common Schr\"{o}dinger type short wave. The results here extend many of the previously obtained results for two-component coupled Schr\"{o}dinger-Korteweg-de Vries systems.