On the modified Korteweg - de Vries equation

Nakao Hayashi, Pavel Naumkin

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We consider the large time asymptotic behavior of solutions to the Cauchy problem for the modified Korteweg - de Vries equation ut + a(t) (u3)x + 1/3Uxxx = O,(t,r) ϵR x R, with initial data u(0,z) = q1(z),z ϵ R.. We assume that the coefficient a(t) ϵ C1(R) is real, bounded and slowly varying function, such that /a'(t)≤C(l + /t/)-7/6. We suppose that the iriitial dah are real ~ valued and small enough, belonging to the weighted Sobolev space. We prove the time decay estimates of the solutims.We also fiud the asympt,otics for large time of the solution in the neighborhood of the self-similar solution.

Original languageEnglish
Title of host publicationInternational Seminar
Subtitle of host publicationDay on Diffraction - Proceedings
EditorsV.E. Grikuro, V.M. Babic, I.V. Androno, V.S. Buldyrev, A.P. Kiselev
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages146-156
Number of pages11
ISBN (Electronic)5799701569, 9785799701567
DOIs
Publication statusPublished - 1999 Jan 1
Externally publishedYes
EventInternational Seminar: Day on Diffraction, IS-DoD 1999 - St. Petersburg, Russian Federation
Duration: 1999 Jun 11999 Jun 3

Publication series

NameInternational Seminar: Day on Diffraction - Proceedings

Conference

ConferenceInternational Seminar: Day on Diffraction, IS-DoD 1999
CountryRussian Federation
CitySt. Petersburg
Period99/6/199/6/3

ASJC Scopus subject areas

  • Radiation
  • Acoustics and Ultrasonics
  • Atomic and Molecular Physics, and Optics

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  • Cite this

    Hayashi, N., & Naumkin, P. (1999). On the modified Korteweg - de Vries equation. In V. E. Grikuro, V. M. Babic, I. V. Androno, V. S. Buldyrev, & A. P. Kiselev (Eds.), International Seminar: Day on Diffraction - Proceedings (pp. 146-156). [816195] (International Seminar: Day on Diffraction - Proceedings). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/DD.1999.816195