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
K SOKALSKI, T WIETECHA, D SOKALSKA
Received 5 November 2003, Accepted 7 October 2004, Available Online 1 February 2005.
- https://doi.org/10.2991/jnmp.2005.12.1.5How to use a DOI?
- 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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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 -