Singular reduction operators in two dimensions

Details Singular reduction operators in two dimensions Singular reduction operators in two dimensions

2008-08-26

arxiv.org/abs/0808.3577v2

J. Phys. A: Math. Theor. 41 (2008) 505201, 24 pp

Mathematics

Analysis of PDEs

22 pages, minor corrections

Scientific paper

10.1088/1751-8113/41/50/505201

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.

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