Variational derivation of improved KP-type of equations


She Liam, Lie and Groesen, E. van (2010) Variational derivation of improved KP-type of equations. Physics Letters A, 374 (3). pp. 411-415. ISSN 0375-9601

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Abstract:The Kadomtsev–Petviashvili equation describes nonlinear dispersive waves which travel mainly in one direction, generalizing the Korteweg–de Vries equation for purely uni-directional waves. In this Letter we derive an improved KP-equation that has exact dispersion in the main propagation direction and that is accurate in second order of the wave height. Moreover, different from the KP-equation, this new equation is also valid for waves on deep water. These properties are inherited from the AB-equation (E. van Groesen, Andonowati, 2007 [1]) which is the unidirectional improvement of the KdV equation. The derivation of the equation uses the variational formulation of surface water waves, and inherits the basic Hamiltonian structure.
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Copyright:© 2010 Elsevier
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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