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PRINCIPLE OF STRUCTURAL ANALOGY OF SOLUTIONS AND ITS APPLICATION TO NONLINEAR PDEs AND DELAY PDEs [PDF]

open access: yesJournal of Mathematical Sciences
Using the principle of structural analogy of solutions, approaches have been developed for constructing exact solutions of complex nonlinear PDEs, including PDEs with delay, based on the use of special solutions to auxiliary simpler related equations. It
Andrei Polyanin
exaly   +2 more sources

Approximate analytical solutions of systems of PDEs by homotopy analysis method [PDF]

open access: yesComputers and Mathematics With Applications, 2008
In this paper, the homotopy analysis method (HAM) is applied to obtain series solutions to linear and nonlinear systems of first- and second-order partial differential equations (PDEs).
Ishak Hashim   +2 more
exaly   +2 more sources
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A method for constructing exact solutions of nonlinear delay PDEs

Journal of Mathematical Analysis and Applications, 2021
Andrei Polyanin, Vsevolod Sorokin
exaly  

Exact Solutions of Reaction–Diffusion PDEs with Anisotropic Time Delay

Mathematics, 2023
Andrei Polyanin, Vsevolod Sorokin
exaly  

New exact solutions of nonlinear wave type PDEs with delay

Applied Mathematics Letters, 2020
Andrei Polyanin, Vsevolod Sorokin
exaly  

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