TRANSFORMATIONS, REDUCTIONS AND EXACT SOLUTIONS OF A HIGHLY NONLINEAR EQUATION OF ELECTRON MAGNETOHYDRODYNAMICS
https://doi.org/10.26583/vestnik.2023.293
Abstract
A strongly nonlinear partial differential equation with three independent variables of the form 𝑢𝑡 = = 𝑢𝑥𝑥𝑢𝑦𝑦−𝑢2𝑥𝑦, which occurs in electron magnetohydrodynamics, isconsidered. Multiparameter transformations that preserve the form of this equation are described, as well as two- and one-dimensional reductions that lead to simpler partial differential equations with two independent variables (including stationary equations of the Monge–Ampere type and nonstationary heat equations) or ordinary differential equations. By methods of generalized separation of variables, exact solutions are constructed, many of which admit representation in elementary functions. More complex solutions are also considered, which are expressed in terms of solutions of linear diffusion-type equations.
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. TRANSFORMATIONS, REDUCTIONS AND EXACT SOLUTIONS OF A HIGHLY NONLINEAR EQUATION OF ELECTRON MAGNETOHYDRODYNAMICS. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2023;12(4):201-210. (In Russ.) https://doi.org/10.26583/vestnik.2023.293
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