On the integrable elliptic cylindrical Kadomtsev-Petviashvili equation
journal contributionposted on 2014-09-01, 12:57 authored by Karima KhusnutdinovaKarima Khusnutdinova, C. Klein, Vladimir S. Matveev, A.O. Smirnov
There exist two versions of the Kadomtsev-Petviashvili (KP) equation, related to the Cartesian and cylindrical geometries of the waves. In this paper, we derive and study a new version, related to the elliptic cylindrical geometry. The derivation is given in the context of surface waves, but the derived equation is a universal integrable model applicable to generic weakly nonlinear weakly dispersive waves. We also show that there exist nontrivial transformations between all three versions of the KP equation associated with the physical problem formulation, and use them to obtain new classes of approximate solutions for water waves. © 2013 American Institute of Physics.
C.K. and V.B.M. thank for financial support by the ANR via the program ANR-09-BLAN-0117-01.
- Mathematical Sciences
Pages? - ? (13)
CitationKHUSNUTDINOVA, K.R. ... et al., 2013. On the integrable elliptic cylindrical Kadomtsev-Petviashvili equation. Chaos, 23, 013126, 13pp.
Publisher© American Institute of Physics
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