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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.

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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