Integrable Dispersive Chains and Their Multi-Phase Solutions

TL;DR

This paper develops multi-phase solutions for integrable dispersive chains linked to a specific 3D degenerate system, providing a broad class of solutions parameterized by many arbitrary parameters and extending to finite component reductions.

Contribution

It introduces a method to construct multi-phase solutions for a class of integrable dispersive chains associated with the Mikhalev system, including their finite component reductions.

Findings

Multi-phase solutions parameterized by infinitely many arbitrary parameters.

Explicit construction of solutions for the Mikhalev system.

Extension of solutions to finite component dispersive reductions.

Abstract

In this paper we construct multi-phase solutions for integrable dispersive chains associated with the three-dimensional linearly degenerate Mikhalev system of first order. These solutions are parameterized by infinitely many arbitrary parameters. As byproduct we describe multi-phase solutions for finite component dispersive reductions of these integrable dispersive chains.