Hamiltonian Perturbations at the Second-Order Approximation
Abstract
Integrability condition of Hamiltonian perturbations of integrable Hamiltonian PDEs of hydrodynamic type up to the second-order approximation is considered. Under a nondegeneracy assumption, we show that the Hamiltonian perturbation at the first-order approximation is integrable if and only if it is trivial, and that under a further assumption, the Hamiltonian perturbation at the second-order approximation is integrable if and only if it is quasi-trivial.
- Publication:
-
Annales Henri Poincaré
- Pub Date:
- December 2020
- DOI:
- 10.1007/s00023-020-00962-w
- arXiv:
- arXiv:2002.00823
- Bibcode:
- 2020AnHP...21.3919Y
- Keywords:
-
- 37K10;
- 37J30;
- 35Q53;
- 37L50;
- Mathematical Physics;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems
- E-Print:
- 17 pages