Dispersionful analogue of the Whitham hierarchy

TL;DR

This paper develops a dispersionful analogue of the Whitham hierarchy using Lax formalism, extending the universal hierarchy to include dispersion effects and illustrating it with key examples.

Contribution

It introduces a novel dispersionful version of the Whitham hierarchy and explores its algebraic reductions, expanding the theoretical framework of integrable systems.

Findings

Formulation of a dispersionful Whitham hierarchy using Lax formalism

Derivation of algebraic orbit finite-field reductions

Illustrative examples demonstrating the theory's applicability

Abstract

The dispersionful analogue, by means of Lax formalism, of the zero-genus universal Whitham hierarchy together with its algebraic orbit finite-field reductions is considered. The theory is illustrated by several significant examples.