The Tsarev Generalized Hodograph Method and Isomonodromic Solutions of Integrable Dispersive Systems

TL;DR

This paper extends the Tsarev Generalized Hodograph Method to dispersive integrable systems, demonstrating that their solutions can be obtained through isomonodromic deformations, linking hydrodynamic systems with complex analysis techniques.

Contribution

It introduces a novel extension of the Tsarev method to dispersive systems using isomonodromic deformations, bridging hydrodynamic and dispersive integrable systems.

Findings

Solutions of dispersive integrable systems can be derived via isomonodromic deformations.

The approach generalizes the classical Tsarev method to a broader class of systems.

The method provides a new perspective on solving complex dispersive equations.

Abstract

General and particular solutions of the so called semi-Hamiltonian hydrodynamic type systems can be obtained by the Tsarev Generalized Hodograph Method. Here we show that a natural extension of this approach applied to dispersive integrable systems is determined by isomonodromic deformations.