Nonclassical symmetries of a class of Burgers' systems
type: Item
instance of: scholarly article
title: Nonclassical symmetries of a class of Burgers' systems
zbMATH Open document ID: 1205.35012
author: D. J. Arrigo
author: David A. Ekrut
author: Jackson R. Fliss
author: Long Le
published in: Journal of Mathematical Analysis and Applications
publication date: 2010-09-01T00:00:00Z
review text: The authors consider the nonclassical symmetries of the Burgers' systems \[ u_t= u_{xx}+ uu_x+ F(u,v)v_x,\qquad v_t= v_{xx}+vv_x+ G(u,v)u_x. \] This study was initiated by \textit{R. Cherniha} and \textit{M. Serov} [J. Math. Anal. Appl. 282, No.~1, 305--328 (2003; Zbl 1073.35192)] but with a restriction on the form of the nonclassical symmetry operator, namely they assume the form \[ \Gamma=\frac{\partial}{\partial t}+ X(t,x,u,v)\frac{\partial}{\partial x}+ U(u,v)\frac{\partial}{\partial u}+ V(u,v)\frac{\partial}{\partial v}. \] Here the authors review the restriction that \(U\) and \(V\) are independent on \(t\) and \(x\) and complete the analysis obtaining only symmetries that are truly nonclassical and inequivalent up to point equivalence transformations.
reviewed by: Svetlana A. Grishina
Mathematics Subject Classification ID: 35B06
Mathematics Subject Classification ID: 35K40
Mathematics Subject Classification ID: 35K58
zbMATH DE Number: 5777355
zbMATH Keywords: Burgers'systems
zbMATH Keywords: nonclassical symmetry
MaRDI profile type: Publication
full work available at URL: j.jmaa.2010.06.026
OpenAlex ID: W2013987284
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DOI: 10.1016/J.JMAA.2010.06.026
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description: scientific article; zbMATH DE number 5777355