Journal of Nonlinear Mathematical Physics

Volume 16, Issue 1, March 2013, 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
Corresponding Author
Ł. Stȩpień
Received 27 November 2007, Accepted 25 June 2008, Available Online 7 January 2021.
DOI
https://doi.org/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/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
16 - 1
Pages
25 - 34
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1142/S1402925109000030How to use a DOI?
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
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  - https://doi.org/10.1142/S1402925109000030
ID  - Stȩpień2021
ER  -