HAMILTONIAN SPATIAL STRUCTURE FOR 3-DIMENSIONAL WATER-WAVES IN A MOVING FRAME OF REFERENCE
UNSPECIFIED. (1994) HAMILTONIAN SPATIAL STRUCTURE FOR 3-DIMENSIONAL WATER-WAVES IN A MOVING FRAME OF REFERENCE. JOURNAL OF NONLINEAR SCIENCE, 4 (3). pp. 221-251. ISSN 0938-8974Full text not available from this repository.
The governing equations for three-dimensional time-dependent water waves in a moving frame of reference are reformulated in terms of the energy and momentum flux. The novelty of this approach is that time-independent motions of the system-that is, motions that are steady in a moving frame of reference-satisfy a partial differential equation, which is shown to be Hamiltonian. The theory of Hamiltonian evolution equations (canonical variables, Poisson brackets, symplectic form, conservation laws) is applied to the spatial Hamiltonian system derived for pure gravity waves. The addition of surface tension changes the spatial Hamiltonian structure in such a way that the symplectic operator becomes degenerate, and the properties of this generalized Hamiltonian system are also studied. Hamiltonian bifurcation theory is applied to the linear spatial Hamiltonian system for capillary-gravity waves, showing how new waves can be found in this framework.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics
T Technology > TJ Mechanical engineering and machinery
Q Science > QC Physics
|Journal or Publication Title:||JOURNAL OF NONLINEAR SCIENCE|
|Number of Pages:||31|
|Page Range:||pp. 221-251|
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