Dynamics of Partial Differential Equations
Volume 20 (2023)
Applications of Nijenhuis geometry IV: Multicomponent KdV and Camassa–Holm equations
Pages: 73 – 98
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 , Harry Dym, coupled Harry Dym , Camassa–Holm, multicomponent Camassa–Holm , Dullin–Gottwald–Holm and Kaup–Boussinesq systems. The series also contains integrable systems with no low-component analogues.
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.
The research of V.M. was supported by DFG grant MA 2565/7.
Received 16 November 2023
Published 23 December 2022