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.
Original language | English (US) |
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Pages (from-to) | 9-29 |
Number of pages | 21 |
Journal | Physica D: Nonlinear Phenomena |
Volume | 203 |
Issue number | 1-2 |
DOIs | |
State | Published - Apr 1 2005 |
Externally published | Yes |
Keywords
- Canonical transformation
- Ill-posedness
- Surface waves
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Applied Mathematics