Journal of Nonlinear Mathematical Physics

Volume 9, Issue 1, February 2002, Pages 11 - 20

The Matrix Kadomtsev­Petviashvili Equation as a Source of Integrable Nonlinear Equations

Authors
Attilio Maccari
Corresponding Author
Attilio Maccari
Received 28 May 2001, Revised 1 August 2001, Accepted 2 August 2001, Available Online 1 February 2002.
DOI
https://doi.org/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.
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
9 - 1
Pages
11 - 20
Publication Date
2002/02
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.2002.9.1.2How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - Attilio Maccari
PY  - 2002
DA  - 2002/02
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  - https://doi.org/10.2991/jnmp.2002.9.1.2
ID  - Maccari2002
ER  -