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Approximate symmetries and conservation laws with applications. (English) Zbl 0989.37076
The authors deal with the theory of approximate symmetries associated with differential equations with a small parameter. They show that approximate conservation laws can be associated with approximate Lie-Bäcklund symmetries for systems which may not possess a Lagrangian. In addition, the authors prove that these conservation laws may be constructed algorithmically which allows them to apply the results to certain classes of linear and nonlinear wave equations.

MSC:
37L20 Symmetries of infinite-dimensional dissipative dynamical systems
37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems
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