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Stepwise asymptotic solutions to the Korteweg-de Vries equation with variable coefficients and a small parameter at the higher-order derivative. (English. Russian original) Zbl 1454.35321

Cybern. Syst. Anal. 56, No. 6, 934-942 (2020); translation from Kibern. Sist. Anal. 2020, No. 6, 86-95 (2020).
Summary: The Korteweg-de Vries equation with variable coefficients and a small parameter of the first level at the higher-order derivative is considered. The concept of a stepwise asymptotic solution is introduced. On the basis of the nonlinear WKB method, an algorithm for creating such solutions is developed and substantiated. The order on small parameter of the asymptotic accuracy of the constructed approximate solution satisfying the original equation is established.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35C08 Soliton solutions
35B40 Asymptotic behavior of solutions to PDEs
35B25 Singular perturbations in context of PDEs
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