EXACT SOLUTIONS AND REDUCTIONS OF UNSTEADY EQUATIONS OF MATHEMATICAL PHYSICS OF THE MONGE – AMPERE TYPE
https://doi.org/10.26583/vestnik.2023.299
EDN: MDGFDG
Abstract
Nonlinear unsteady equations of mathematical physics with three independent variables containing the first derivative in time and a quadratic combination of the second derivatives in spatial variables of the Monge – Ampere type are investigated. Separate equations of this type are found, for example, in electron magnetohydrodynamics and differential geometry. In this paper, an eleven-parameter transformation preserving the form of the class of nonlinear equations under study is described. Two-dimensional and one-dimensional reductions leading to simpler partial differential equations with two independent variables or ordinary differential equations are considered. Self-similar and other invariant solutions are obtained. By methods of generalized separation of variables, a number of exact solutions are constructed, many of which are expressed in terms of elementary functions.
Keywords
nonlinear equations of mathematical physics,
unsteady equations of the Monge – Ampere type,
magnetohydrodynamics,
exact solutions,
self-similar and invariant solutions,
generalized separable solutions,
solutions in elementary functions,
one-dimensional and two-dimensional reductions
Supporting agencies: The work was carried out on the topic of a state assignment (state registration number 123021700057-0).
About the Author
A. D. Polyanin
Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences
Russian Federation
Russian Federation
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For citations:
Polyanin A.D. EXACT SOLUTIONS AND REDUCTIONS OF UNSTEADY EQUATIONS OF MATHEMATICAL PHYSICS OF THE MONGE – AMPERE TYPE. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2023;12(5):276-288. (In Russ.) https://doi.org/10.26583/vestnik.2023.299. EDN: MDGFDG
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