## One Citation

### Existence of Generalized Solitary Wave Solutions of the Coupled KdV–CKdV System

- MathematicsQualitative Theory of Dynamical Systems
- 2022

This paper studies the traveling wave solutions of the coupled KdV–CKdV system ut+2buξ+auξξξ=-2b(uv)ξ,vt+bvξ+bvvξ+cvξξξ=-b(|u|2)ξ,\documentclass[12pt]{minimal} \usepackage{amsmath}…

## 23 References

### The interaction of long and short waves in dispersive media

- Physics
- 2016

The KdV equation models the propagation of long waves in dispersive media, while the NLS equation models the dynamics of narrow-bandwidth wave packets consisting of short dispersive waves. A system…

### Existence and Stability of a Two-Parameter Family of Solitary Waves for an NLS-KdV System

- MathematicsAdvances in Differential Equations
- 2013

We prove existence and stability results for a two-parameter family of solitary-wave solutions to a system in which an equation of nonlinear Schr\"odinger type is coupled to an equation of…

### Conservation and Scattering in Nonlinear Wave Systems

- Physics
- 1993

Perturbational approaches have a long history of application to dynamical systems. A special role in this subject belongs to Hamiltonian systems with a small parameter 6, which are integrable when 6…

### STABILITY OF SOLITARY WAVE SOLUTIONS FOR EQUATIONS OF SHORT AND LONG DISPERSIVE WAVES

- Mathematics
- 2006

In this paper, we consider the existence and stability of a novel set of solitary-wave solutions for two models of short and long dispersive waves in a two layer fluid. We prove the existence of…

### Solitons and the Inverse Scattering Transform

- Physics
- 2012

Dispersion and nonlinearity play a fundamental role in wave motions in nature. The nonlinear shallow water equations that neglect dispersion altogether lead to breaking phenomena of the typical…

### A Simple model of the integrable Hamiltonian equation

- Physics, Mathematics
- 1978

A method of analysis of the infinite‐dimensional Hamiltonian equations which avoids the introduction of the Backlund transformation or the use of the Lax equation is suggested. This analysis is based…

### Well-posedness for the Schrödinger-Korteweg-de Vries system

- Mathematics
- 2007

We study well-posedness of the Cauchy problem associated to the Schrodinger-Korteweg-de Vries system. We obtain local well-posedness for weak initial data, where the best result obtained is for data…