2011
Hamiltonian form and solitary waves of the spatial Dysthe equations
JJETP Letters
F. Fedele and D. Dutykh
JETP Letters 94(12): 921-925 (2011)
Open Access
Abstract
The spatial Dysthe equations describe the envelope evolution of the free-surface and potential of gravity waves in deep waters. Their Hamiltonian structure and new invariants are unveiled by means of a gauge transformation to a new canonical form of the evolution equations. An accurate Fourier-type spectral scheme is used to solve for the wave dynamics and validate the new conservation laws, which are satisfied up to machine precision. Traveling waves are numerically constructed using the Petviashvili method. It is shown that their collision appears inelastic, suggesting the non-integrability of the Dysthe equations.
Keywords
Solitary wavesGravity wavesSpatial dynamicsground stateHamiltonianDysthe equationWave dynamicssolitary waveFree-surface wavesDysthe equationsdeep waterNon-integrabilitySpectral methodstraveling waveHamiltonian mechanicsPetviashvili method
Bibliographic record
BibTeX Citation
@article{Fedele2011hamiltonianform,
author = {Fedele, F. and Dutykh, D.},
title = {Hamiltonian form and solitary waves of the spatial Dysthe equations},
journal = {JETP Letters},
year = {2011},
volume = {94},
number = {12},
pages = {921--925},
doi = {10.1134/S0021364011240039},
abstract = {The spatial Dysthe equations describe the envelope evolution of the free-surface and potential of gravity waves in deep waters. Their Hamiltonian structure and new invariants are unveiled by means of a gauge transformation to a new canonical form of the evolution equations. An accurate Fourier-type spectral scheme is used to solve for the wave dynamics and validate the new conservation laws, which are satisfied up to machine precision. Traveling waves are numerically constructed using the Petviashvili method. It is shown that their collision appears inelastic, suggesting the non-integrability of the Dysthe equations.},
keywords = {Solitary waves, Gravity waves, Spatial dynamics, ground state, Hamiltonian, Dysthe equation, Wave dynamics, solitary wave, Free-surface waves, Dysthe equations, deep water, Non-integrability, Spectral methods, traveling wave, Hamiltonian mechanics, Petviashvili method}
}