Automatic Construction of Newton Polygons Corresponding to Polynomial Ordinary Differential Equations
https://doi.org/10.1134/S2304487X19030088
Abstract
The ACNP (automatic construction of Newton polygons) program designed to automatically construct Newton polygons corresponding to polynomial differential equations has been described. A Newton polygon of an ordinary differential equation is a convex polygon whose vertices are the outer points of the carrier of this equation (the carrier is the set of points on the plane corresponding to the monomials of the differential equation according to a certain rule). Newton polygons for polynomial ordinary differential equations are useful for studying the integrability of nonlinear equations using the Kovalevskaya algorithm, for constructing asymptotic solutions, and for finding exact solutions of nonlinear differential equations. Automatic construction of Newton polygons in some cases allows finding the order of the pole of the equation, select the leading terms of the equation, speed up the process of finding the power asymptotic behavior of solutions of differential equations, and simplify the choice of the simplest equation when finding exact solutions of nonlinear differential equations. The ACNP program is written in the Maple computer algebra environment. The algorithm of the program and examples of its application have been presented.
Keywords
Newton polygons,
exact solutions of differential equations,
Painlevé property test,
power-law asymptotic behavior
Supporting agencies: The research was carried out at the expense of 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. Automatic Construction of Newton Polygons Corresponding to Polynomial Ordinary Differential Equations. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2019;8(3):283-288. (In Russ.) https://doi.org/10.1134/S2304487X19030088
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