Applications of Nijenhuis Geometry IV: multicomponent KdV and Camassa-Holm equations

TL;DR

This paper develops a new series of multicomponent integrable PDE systems, unifying many well-known equations like KdV and Camassa-Holm, and introduces novel systems without low-component counterparts.

Contribution

It constructs a comprehensive series of multicomponent integrable PDEs, expanding the landscape of integrable systems with new examples and generalizations.

Findings

Includes many famous integrable systems as special cases

Introduces new integrable systems with no low-component analogues

Provides a unified framework for multicomponent integrable PDEs

Abstract

We construct a new series of multicomponent integrable PDE systems that contain as particular example (with appropriately chosen parameters) many famous integrable systems including KdV, coupled KdV, Harry Dym, coupled Harry Dym, Camassa-Holm, multicomponent Camassa-Holm, Kaup-Boussinesq systems. The series contains also integrable systems with no low-component analogues.