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ВИДЕОТЕКА |
Dynamics in Siberia - 2019
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A new class of exact solutions for three-dimensional quasilinear systems of first order М. В. Павлов |
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Аннотация: Well-known Lin–Reissner–Tsien equation in aerodynamics (1948) will be considered. This equation also is known as the Khokhlov–Zabolotskaya equation in nonlinear acoustics, and is known as a dispersionless limit of the Kadomtsev–Petviashvili equation in hydrodynamics. New ansatz for construction of infinitely many two-dimensional reductions is found for this three-dimensional equation. They are generalisations of two-dimensional hydrodynamic reductions. In one-component case, a corresponding particular solution is found with five arbitrary functions of a single variable. Also some other three-dimensional integrable quasilinear systems of first order will be considered. Язык доклада: английский |