Dynamics of Partial Differential Equations

Volume 20 (2023)

Number 1

Applications of Nijenhuis geometry IV: Multicomponent KdV and Camassa–Holm equations

Pages: 73 – 98

DOI: https://dx.doi.org/10.4310/DPDE.2023.v20.n1.a4

Authors

Alexey V. Bolsinov (Department of Mathematical Sciences, Loughborough University, Loughborough, United Kingdom)

Andrey Yu. Konyaev (Faculty of Mechanics and Mathematics, Moscow State University, Moscow, Russia; and Moscow Center for Fundamental and Applied Mathematics, Moscow, Russia)

Vladimir S. Matveev (Institut für Mathematik, Friedrich Schiller Universität Jena, Germany)

Abstract

We construct a new series of multi-component integrable PDE systems that contains as particular examples (with appropriately chosen parameters) and generalises many famous integrable systems including KdV, coupled KdV [1], Harry Dym, coupled Harry Dym [2], Camassa–Holm, multicomponent Camassa–Holm [14], Dullin–Gottwald–Holm and Kaup–Boussinesq systems. The series also contains integrable systems with no low-component analogues.

Keywords

multicomponent integrable PDE systems, Korteweg–de Vries equation, Camassa–Holm equation, Harry Dym equation, Nijenhuis operator, evolutionary flow, conservation laws and symmetries

2010 Mathematics Subject Classification

Primary 37K10, 37K25, 37-xx, 53B50. Secondary 53A55, 53B20, 53D17.

Full Text (PDF format)

The research of V.M. was supported by DFG grant MA 2565/7.

Received 16 November 2023

Published 23 December 2022