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Please use this identifier to cite or link to this item: https://dspace.lboro.ac.uk/2134/15723

Title: On the integrable elliptic cylindrical Kadomtsev-Petviashvili equation
Authors: Khusnutdinova, Karima R.
Klein, C.
Matveev, Vladimir S.
Smirnov, A.O.
Issue Date: 2013
Publisher: © American Institute of Physics
Citation: KHUSNUTDINOVA, K.R. ... et al., 2013. On the integrable elliptic cylindrical Kadomtsev-Petviashvili equation. Chaos, 23, 013126, 13pp.
Abstract: 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.
Description: Copyright (2013) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.
Sponsor: C.K. and V.B.M. thank for financial support by the ANR via the program ANR-09-BLAN-0117-01.
Version: Published
DOI: 10.1063/1.4792268
URI: https://dspace.lboro.ac.uk/2134/15723
Publisher Link: http://dx.doi.org/10.1063/1.4792268
ISSN: 1054-1500
Appears in Collections:Published Articles (Maths)

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