Affiliation:
1. Department of Applied Mathematics, University of Colorado at Boulder, 526 UCB, Boulder, CO 80309-0526, USA
Abstract
A nonlocal spectral formulation of classic water waves is derived, and its connection to the classic water wave equations and the Dirichlet–Neumann operator is explored. The nonlocal spectral formulation is also extended to a two-fluid system with a free interface, from which long wave asymptotic reductions are obtained. Of particular interest is an asymptotically distinguished (2 + 1)-dimensional generalization of the intermediate long wave equation, which includes the Kadomtsev–Petviashvili equation and the Benjamin–Ono equation as limiting cases. Lump-type solutions to this (2 + 1)-dimensional ILW equation are obtained, and the speed versus amplitude relationship is shown to be linear in the shallow, intermediate, and deep water regimes.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Analysis
Cited by
15 articles.
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