On optimal canonical variables in the theory of ideal fluid with free surface
Abstract
Dynamics of ideal fluid with free surface can be effectively solved by perturbing the Hamiltonian in weak nonlinearity limit. However it is shown that perturbation theory, which includes third and fourth order terms in the Hamiltonian, results in the ill-posed equations because of short wavelength instability. To fix that problem we introduce the canonical Hamiltonian transformation from original physical variables to new variables for which instability is absent.
- Publication:
-
Physica D Nonlinear Phenomena
- Pub Date:
- April 2005
- DOI:
- 10.1016/j.physd.2005.02.010
- arXiv:
- arXiv:nlin/0410054
- Bibcode:
- 2005PhyD..203....9L
- Keywords:
-
- Nonlinear Sciences - Pattern Formation and Solitons;
- Physics - Atmospheric and Oceanic Physics;
- Physics - Computational Physics;
- Physics - Fluid Dynamics
- E-Print:
- 23 page, 6 figures, submitted to Physica D