Automation of the Construction of Exact Solutions of Nonlinear Differential Equations
https://doi.org/10.1134/S2304487X19060038
Abstract
The AFES program (automatic finding exact solutions) designed to find exact solutions of polinomial ordinary differential equations has been described. The simplest equations method has been used to find exact solutions. The method consists in constructing exact solutions of differential equations using a general solution of a lower order differential equation. In order to choose the form of the exact solution, it is necessary to determine the pole order of the solution of the original equation and the pole order of the solution of the simplest equation. The program for automatically constructing Newton polygons ACNP (automatic construction of Newton polygons) has been used. The Riccati equation and the equation for the elliptic Weierstrass function have been considered as simple equations. In order to test the program, examples of constructing exact solutions of various nonlinear differential equations are given. The AFES program is written in the Maple computer algebra system. The algorithm of the program and examples of its application are given. The AFES program has several advantages over wellknown programs for finding exact solutions of differential equations. In particular, constructed exact solutions are different and they cannot be transformed to each other.
Keywords
Supporting agencies: The study was supported by a grant from the Russian Science Foundation (Project No. 18-11-00209)
About the Authors
N. A. Kudryashov
National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)
Russian Federation
Russian Federation
115409
Moscow
A. A. Kutukov
National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)
Russian Federation
Russian Federation
115409
Moscow
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Review
For citations:
Kudryashov N.A., Kutukov A.A. Automation of the Construction of Exact Solutions of Nonlinear Differential Equations. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2019;8(6):533-539. (In Russ.) https://doi.org/10.1134/S2304487X19060038
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