Opportunity of representation of the nonlinear wave equations through a variable action-angle

TL;DR

This paper explores a method to represent solutions of nonlinear wave equations, including stationary solitary waves, as systems of ordinary differential equations using variable action-angle coordinates.

Contribution

It introduces a novel approach to express nonlinear wave solutions in terms of variable action-angle variables, facilitating analysis and solution of these equations.

Findings

Representation of solitary waves as ODE systems in action-angle variables

Enhanced understanding of nonlinear wave dynamics

Potential for simplified solution methods

Abstract

The approach allowing is considered to represent the solutions such as stationary lonely waves of various nonlinear wave the equations as system of the ordinary differential equations in variable action - angle.