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

DOI10.4310/DPDE.2023.V20.N1.A4zbMATH Open1517.37067arXiv2206.12942MaRDI QIDQ6403187

A. V. Bolsinov, Vladimir Matveev, Andrey Yu. Konyaev

Publication date: 26 June 2022

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.

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Applications of differential geometry to physics (53Z05) Soliton equations (35Q51) Poisson manifolds; Poisson groupoids and algebroids (53D17) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25) Local Riemannian geometry (53B20) Differential invariants (local theory), geometric objects (53A55)

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