CONSTRUTING SOLUTIONS TO NONLINEAR EQUATIONS OF MATHEMATIСAL PHYSIСS USING EXAСT SOLUTIONS TO SIMPLER EQUATIONS
https://doi.org/10.26583/vestnik.2024.318
EDN: JGRBCV
Abstract
A method has been developed for constructing exact solutions of complex nonautonomous nonlinear equations of mathematical physics, the coefficients of which explicitly depend on time, by using solutions with generalized or functional separation of variables of simpler autonomous equations of mathematical physics, the coefficients of which do not depend on time. Specific examples of constructing exact solutions of nonlinear equations of mathematical physics, the coefficients of which depend arbitrarily on time, are considered. It is shown that solutions with generalized and functional separation of variables of nonlinear equations of mathematical physics with constant delay can be used to construct exact solutions of more complex nonlinear equations of mathematical physics with variable delay of a general form. A number of nonlinear reaction-diffusion equations with variable delay are described, which allow exact solutions with generalized separation of variables
Keywords
nonlinear equations of mathematical physics,
partial differential equations with delay,
solution methods,
exact solutions,
generalized separable solutions,
functional separable solutions
Supporting agencies: The work was carried out on the topic of a state assignment (state registration number 124012500440-9).
About the Author
A. D. Polyanin
Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences
Russian Federation
Russian Federation
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Review
For citations:
Polyanin A.D. CONSTRUTING SOLUTIONS TO NONLINEAR EQUATIONS OF MATHEMATIСAL PHYSIСS USING EXAСT SOLUTIONS TO SIMPLER EQUATIONS. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2024;13(2):66-75. (In Russ.) https://doi.org/10.26583/vestnik.2024.318. EDN: JGRBCV
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