Algorithm for Constructing the First Integrals for One Class of Nonlinear Differential Equations of the Second Order
https://doi.org/10.56304/S2304487X22020080
Abstract
An algorithm for constructing the first integrals of one class of nonlinear ordinary differential equations of the second order is proposed. Special approaches such as the simplest equation method are usually used to find analytical solutions of these equations. The proposed algorithm makes it possible to find general solutions of nonlinear differential equations in some cases. The algorithm is illustrated in application to the complex Ginzburg–Landau equation. The solution of this equation is sought using traveling wave variables. It is shown that the proposed algorithm allows one to reduce a rather complex nonlinear ordinary differential equation of the second order to a first order differential equation, the general solution of which can be represented as a quadrature. With some restrictions on the arbitrary constants, the solution of the Ginzburg–Landau equation can be presented in the form of an analytical expression.
About the Author
N. A. Kudryashov
National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)
Russian Federation
Russian Federation
Moscow, 115409
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Review
For citations:
Kudryashov N.A. Algorithm for Constructing the First Integrals for One Class of Nonlinear Differential Equations of the Second Order. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2022;11(2):109–116. (In Russ.) https://doi.org/10.56304/S2304487X22020080
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