Volume 16, Issue 1, March 2009, Pages 25 - 34
The Bogomolny Decomposition for Systems of Two Generalized Nonlinear Partial Differential Equations of the Second Order
Authors
Ł. Stȩpień†, ¶, D. Sokalska‡, ‖, K. Sokalski§, **
†Department of Computer Sciences and Computer Methods, Pedagogical University of Cracow, 30-084 Kraków, ul. Podchorażych 2, Poland
‡Institute of Physics, Technical University of Cracow, 30-084 Kraków, ul. Podchorażych 1, Poland
§Institute of Computer Science, Technical University of Czȩstochowa, 42-200 Czȩstochowa, al. Armii Krajowej 17, Poland
Received 27 November 2007, Accepted 25 June 2008, Available Online 7 January 2021.
- DOI
- 10.1142/S1402925109000030How to use a DOI?
- Keywords
- Nonlinear partial differential equations; variational methods; Bogomolny decomposition
- Abstract
Using a concept of strong necessary conditions we derive the Bogomolny decomposition for systems of two generalized elliptic and parabolic nonlinear partial differential equations (NPDE) of the second order. The generalization means that the equation coefficients depend on the field variables. According to the Cinquini-Cibrario criteria [18–20] the first type is characterized to be an elliptic, whereas the second one is a parabolic system. As a result we derive conditions for existence of the Bogomolny relationships.
- Copyright
- © 2009 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Ł. Stȩpień AU - D. Sokalska AU - K. Sokalski PY - 2021 DA - 2021/01/07 TI - The Bogomolny Decomposition for Systems of Two Generalized Nonlinear Partial Differential Equations of the Second Order JO - Journal of Nonlinear Mathematical Physics SP - 25 EP - 34 VL - 16 IS - 1 SN - 1776-0852 UR - https://doi.org/10.1142/S1402925109000030 DO - 10.1142/S1402925109000030 ID - Stȩpień2021 ER -