Jacobian Elliptic Wave Solutions for the Wadati-Segur-Ablowitz Equation

TL;DR

This paper derives Jacobian elliptic wave solutions for a Hamiltonian amplitude equation related to wave train instabilities, showing how solutions transition from trivial to solitary forms as the elliptic parameter varies.

Contribution

It introduces a method to obtain Jacobian elliptic solutions for a new Hamiltonian amplitude equation, linking trivial and solitary wave solutions through parameter variation.

Findings

Solutions transform from trivial to solitary as parameter varies.

Provides explicit Jacobian elliptic wave solutions for the equation.

Connects wave train instabilities with elliptic function solutions.

Abstract

Jacobian elliptic travelling wave solutions for a new Hamiltonian amplitude equation determining some instabilities of modulated wave train are obtained. By mere variation of the Jacobian elliptic parameter $k^2$ from zero to one, these solutions are transformed from a trivial one to the known solitary solutions.