The deformation of the Whitham systems in the almost linear case

TL;DR

This paper develops a modified deformation scheme for Whitham systems that remains stable when the initial system is nearly linear, addressing a gap in the stability of existing methods.

Contribution

It introduces a new deformation scheme specifically designed for almost linear initial systems, ensuring stability in the linear limit.

Findings

The proposed scheme stabilizes Whitham system deformations near linearity.

Standard deformation procedures become unstable in the linear limit, necessitating the new approach.

The method enhances the robustness of Whitham system analysis in near-linear regimes.

Abstract

We consider the deformation of the Whitham systems in the case when the initial system is close to linear one. It appears that the deformation procedure should be modified in this special case to make all the constructions stable in the linear limit. We suggest here the special deformation scheme which gives the stable deformation of the Whitham system for the almost linear initial systems.