517.9 Methods of functional separation of variables and their application in mathematical physics

Polyanin A. D. (Bauman Moscow State Technical University/Ishlinsky Institute for Problems in Mechanics/MEPhI)

NONLINEAR EQUATIONS OF MATHEMATICAL PHYSICS, FUNCTIONAL SEPARATION OF VARIABLES, GENERALIZED SEPARATION OF VARIABLES, EXACT SOLUTIONS, NONLINEAR REACTION-DIFFUSION EQUATIONS


doi: 10.18698/2309-3684-2019-1-6597


A brief review of existing modifications of the method of functional separation of varia-bles is given. A new more general approach is proposed for construction of ex-act solu-tions of nonlinear equations of mathematical physics and mechanics, which is based on implicit transformations of integral type in combination using the split-ting principle. The effectiveness of this approach is illustrated on nonlinear diffusion equations that contain reaction and convective terms with variable coefficients. The focus is on equations of a fairly general form that depend on two or three arbitrary functions (such nonlinear equations are the most difficult to analyze). Many new exact solutions with functional separation of variables and generalized traveling wave type solutions are described. The obtained solutions can be used to test various numerical and approximate analytical methods of mathematical physics


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Работа выполнена по теме государственного задания (№ госрегистрации AAAA-A17-117021310385-6) и при частичной финансовой поддержке Российского фонда фундаментальных исследований (проект № 18-29-03228).


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