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Ukrainian Mathematical Journal

, Volume 66, Issue 12, pp 1842–1861 | Cite as

Asymptotic Multiphase Solitonlike Solutions of the Cauchy Problem for a Singularly Perturbed Korteweg–de-Vries Equation with Variable Coefficients

  • V. H. Samoylenko
  • Yu. I. Samoylenko
Article
  • 37 Downloads

We describe the set of initial conditions under which the Cauchy problem for a singularly perturbed Korteweg–de-Vries equation with variable coefficients has an asymptotic multiphase solitonlike solution. The notion of manifold of initial values for which the above-mentioned solution exists is proposed for the analyzed Cauchy problem. The statements on the estimation of the difference between the exact and constructed asymptotic solutions are proved for the Cauchy problem.

Keywords

Cauchy Problem Asymptotic Solution Burger Equation Vries Equation Singular Part 
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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • V. H. Samoylenko
    • 1
  • Yu. I. Samoylenko
    • 1
  1. 1.Shevchenko National University of KyivKyivUkraine

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