On the systematic approach to the classification of differential equations by group theoretical methods. (English) Zbl 1173.35318
Summary: Complete symmetry groups enable one to characterise fully a given differential equation. By considering the reversal of an approach based upon complete symmetry groups we construct new classes of differential equations which have the equations of Bateman, Monge-Ampère and Born-Infeld as special cases. We develop a symbolic algorithm to decrease the complexity of the calculations involved.
MSC:
| 35A30 | Geometric theory, characteristics, transformations in context of PDEs |
| 58J70 | Invariance and symmetry properties for PDEs on manifolds |
Keywords:
complete symmetry groups; Lie remarkability; Monge-Ampère; Bateman and Born-Infeld equationsSoftware:
SYMReferences:
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