Symmetry and exact solutions of multidimensional nonlinear wave equations (Q1097412)
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scientific article; zbMATH DE number 4034239
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Symmetry and exact solutions of multidimensional nonlinear wave equations |
scientific article; zbMATH DE number 4034239 |
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Symmetry and exact solutions of multidimensional nonlinear wave equations (English)
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1987
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The paper is dedicated to the extension of the asymptotic Krylov- Bogoljubov method for nonlinear partial differential equations. A survey of some results in this field is given. Using group transforms the family of exact solutions of a multidimensional nonlinear wave equation with nontrivial symmetry properties is constructed. The conditions of invariance of this equation with respect to a Lie algebra are found. A number of the well-known equations of mathematical physics are exactly solved by means of special construction of their solutions. 18 references fully cover the stated problem.
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asymptotic Krylov-Bogoljubov method
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group transforms
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exact solutions
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nonlinear wave equation
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symmetry properties
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invariance
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