Integrable systems of the intermediate long wave type in 2 + 1 dimensions
Abstract
We classify 2 + 1 dimensional integrable systems with nonlocality of the intermediate long wave type. Links to the 2 + 1 dimensional waterbag system are established. Dimensional reductions of integrable systems constructed in this paper provide dispersive regularisations of hydrodynamic equations governing propagation of long nonlinear waves in a shear flow with piecewise linear velocity profile (for special values of vorticities).
- Publication:
-
Physica D Nonlinear Phenomena
- Pub Date:
- July 2022
- DOI:
- 10.1016/j.physd.2022.133310
- arXiv:
- arXiv:2106.09602
- Bibcode:
- 2022PhyD..43533310G
- Keywords:
-
- Multi-dimensional integrable systems;
- Hydrodynamic reductions;
- Dispersive deformations;
- Lax pairs;
- Waterbag system;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems;
- Mathematical Physics;
- 35Q55;
- 37K10
- E-Print:
- 15 pages