The Matrix Kadomtsev­Petviashvili Equation as a Source of Integrable Nonlinear Equations

DOI

10.2991/jnmp.2002.9.1.2How to use a DOI?

Abstract

A new integrable class of Davey­Stewartson type systems of nonlinear partial diffrential equations (NPDEs) in 2+1 dimensions is derived from the matrix Kadomtsev­ Petviashvili equation by means of an asymptotically exact nonlinear reduction method based on Fourier expansion and spatio-temporal rescaling. The integrability by the inverse scattering method is explicitly demonstrated, by applying the reduction tecnique also to the Lax pair of the starting matrix equation and thereby obtaining the Lax pair for the new class of systems of equations. The characteristics of the redution method suggest that the new systems are likely to be of applicative relevance. A reduction to a system of two interacting complex fields is briefly described.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Attilio Maccari
PY  - 2002
DA  - 2002/02/01
TI  - The Matrix Kadomtsev­Petviashvili Equation as a Source of Integrable Nonlinear Equations
JO  - Journal of Nonlinear Mathematical Physics
SP  - 11
EP  - 20
VL  - 9
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2002.9.1.2
DO  - 10.2991/jnmp.2002.9.1.2
ID  - Maccari2002
ER  -