On simultaneous solution of the KdV equation and a fifth-order differential equation

Authors

  • R.N. Garifullin
    Institution of Russian Academy of Sciences Institute of Mathematics with Computer Center, Ufa
    Bashkir State University, Ufa

DOI:

https://doi.org/10.13108/2016-8-4-52

Keywords:

asymptotics, matching of asymptotic expansions, Korteweg–de Vries equation, non-dissipative shock waves.

Abstract

In the paper we consider an universal solution to the KdV equation. This solution also satisfies a fifth order ordinary differential equation. We pose the problem on studying the behavior of this solution as t\to\infty. For large time, the asymptotic solution has different structure depending on the slow variable s=x^2/t. We construct the asymptotic solution in the domains s<-3/4, $-3/4

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Published

20.12.2016