Method of Functional Separation of Variables Can Give More Exact Solutions than Methods Based on a Single Differential Constraint
https://doi.org/10.1134/S2304487X19050067
Abstract
It is shown that the direct method of functional separation of variables can sometimes provide a larger number of exact solutions of nonlinear partial differential equations than the method of differential constraints (with a single constraint) and the nonclassical method of symmetry reduction (based on the invariant surface condition). This fact is illustrated on nonlinear reaction–diffusion and convection–diffusion equations with variable coefficients, nonlinear Klein–Gordon type equations, and hydrodynamic boundary layer equations. Some new exact solutions are given.
Keywords
direct method of functional separation of variables,
method of differential constraints,
nonclassical method of symmetry reduction,
direct method of Clarkson and Kruskal,
exact solutions
Supporting agencies: The work was carried out on the topic of the state task (state registration number AAAA-A17-117021310385- 6) and with partial financial support from the Russian Foundation for Basic Research (project No. 18-29-10025)
About the Author
A. D. Polyanin
Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences; National Research Nuclear University MEPhI (Moscow Engineering Physics Institute); Bauman Moscow State Technical University
Russian Federation
Russian Federation
119526
115409
105005
Moscow
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For citations:
Polyanin A.D. Method of Functional Separation of Variables Can Give More Exact Solutions than Methods Based on a Single Differential Constraint. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2019;8(5):445-452. (In Russ.) https://doi.org/10.1134/S2304487X19050067
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