Journal of Nonlinear Mathematical Physics

Volume 12, Issue 1, February 2005, Pages 31 - 52

Existence of Dual Equations by Means of Strong Necessary Conditions - Analysis of Integrability of Partial Differential Nonlinear Equations

Authors
K SOKALSKI, T WIETECHA, D SOKALSKA
Corresponding Author
K SOKALSKI
Available Online 1 February 2005.
DOI
https://doi.org/10.2991/jnmp.2005.12.1.5How to use a DOI?
Abstract
A concept of strong necessary conditions for extremum of functional has been aplied for analysis an existence of dual equations for a system of two nonlinear Partial Differential Equations (PDE) in 1+1 dimensions. We consider two types of the dual equations: the Bäcklund transformations and the Bogomolny equations. A general form of the second order PDE with a derivative-less non-linear term has been cosidered. In the case of a coupled system of equations the general conditions for the existence of the Bogomolny decomposition are derived. In the case of an uncoupled system of equations the Bogomolny equations become the Bäcklund transformations. It has been found a denumerable classes of coupled systems possessing the Bogomolny relationship. Weaken the method into semi-strong necessary conditions is presented together with an application to the Lax hierarchy. The method basing on both the strong and the semi-strong necessary condition concept reduces the derivation of the dual equations to an algorithm.
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
12 - 1
Pages
31 - 52
Publication Date
2005/02
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.2005.12.1.5How 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  - K SOKALSKI
AU  - T WIETECHA
AU  - D SOKALSKA
PY  - 2005
DA  - 2005/02
TI  - Existence of Dual Equations by Means of Strong Necessary Conditions - Analysis of Integrability of Partial Differential Nonlinear Equations
JO  - Journal of Nonlinear Mathematical Physics
SP  - 31
EP  - 52
VL  - 12
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2005.12.1.5
DO  - https://doi.org/10.2991/jnmp.2005.12.1.5
ID  - SOKALSKI2005
ER  -