Singular reduction operators in two dimensions

2008/08/31 by Michael Kunzinger, Roman O. Popovych · 2 citations
Mathematics · Physics and Astronomy · #math.AP #math-ph #math.MP #msc:35A30 #msc:35C05 #msc:35K55 #msc:35L70

paper · pdf · doi:10.1088/1751-8113/41/50/505201

published as J. Phys. A: Math. Theor. 41 (2008) 505201, 24 pp · 22 pages, minor corrections

arxiv created 2008/11/04 · arxiv updated 2009/12/01

Abstract

The notion of singular reduction operators, i.e., of singular operators of nonclassical (conditional) symmetry, of partial differential equations in two independent variables is introduced. All possible reductions of these equations to first-order ODEs are are exhaustively described. As examples, properties of singular reduction operators of (1+1)-dimensional evolution and wave equations are studied. It is shown how to favourably enhance the derivation of nonclassical symmetries for this class by an in-depth prior study of the corresponding singular vector fields.

Cited by

• Group-theoretical analysis of variable coefficient nonlinear telegraph equations
• Singular reduction modules of differential equations

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