On Optimal Canonical Variables in the Theory of Ideal Fluid with Free Surface

Details On Optimal Canonical Variables in the Theory of Ideal Fluid with Free Surface On Optimal Canonical Variables in the Theory of Ideal Fluid with Free Surface

2004-10-25

arxiv.org/abs/nlin/0410054v1

Physica D, v. 203, pp. 9-29 (2005).

Nonlinear Sciences

Pattern Formation and Solitons

23 page, 6 figures, submitted to Physica D

Scientific paper

10.1016/j.physd.2005.02.010

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 transform from original physical variables to new variables for which instability is absent.

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