Factorization technique for the modified Korteweg-de Vries equation

Nakao Hayashi; Pavel I. Naumkin

Factorization technique for the modified Korteweg-de Vries equation

Nakao Hayashi, Pavel I. Naumkin

Research Alliance Center for Mathematical Sciences (RACMaS)

Research output: Contribution to journal › Article › peer-review

12 Citations (Scopus)

Abstract

We study the large time asymptotics of solutions to the Cauchy problem for the modified Korteweg-de Vries equation (Formula presented) We develop the factorization technique to obtain the large time asymptotics of solutions in the neighborhood of the self-similar solution in the case of nonzero total mass initial data. Our result is an improvement of the previous work [18].

Original language	English
Pages (from-to)	49-95
Number of pages	47
Journal	SUT Journal of Mathematics
Volume	52
Issue number	1
Publication status	Published - 2016

Keywords

Large time asymptotics
Modified Korteweg-de Vries equation
Self-similar solution

ASJC Scopus subject areas

Mathematics(all)

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title = "Factorization technique for the modified Korteweg-de Vries equation",

abstract = "We study the large time asymptotics of solutions to the Cauchy problem for the modified Korteweg-de Vries equation (Formula presented) We develop the factorization technique to obtain the large time asymptotics of solutions in the neighborhood of the self-similar solution in the case of nonzero total mass initial data. Our result is an improvement of the previous work [18].",

keywords = "Large time asymptotics, Modified Korteweg-de Vries equation, Self-similar solution",

author = "Nakao Hayashi and Naumkin, {Pavel I.}",

note = "Funding Information: We are grateful to an unknown referee for many useful suggestions and comments and letting us know the recent papers [9] and [11]. The work of N.H. is partially supported by JSPS KAKENHI Grant Numbers 25220702, 15H03630. The work of P.I.N. is partially supported by CONACYT and PAPIIT project IN100616.",

year = "2016",

language = "English",

volume = "52",

pages = "49--95",

journal = "SUT Journal of Mathematics",

issn = "0916-5746",

publisher = "Science University of Tokyo",

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TY - JOUR

T1 - Factorization technique for the modified Korteweg-de Vries equation

AU - Hayashi, Nakao

AU - Naumkin, Pavel I.

N1 - Funding Information: We are grateful to an unknown referee for many useful suggestions and comments and letting us know the recent papers [9] and [11]. The work of N.H. is partially supported by JSPS KAKENHI Grant Numbers 25220702, 15H03630. The work of P.I.N. is partially supported by CONACYT and PAPIIT project IN100616.

PY - 2016

Y1 - 2016

N2 - We study the large time asymptotics of solutions to the Cauchy problem for the modified Korteweg-de Vries equation (Formula presented) We develop the factorization technique to obtain the large time asymptotics of solutions in the neighborhood of the self-similar solution in the case of nonzero total mass initial data. Our result is an improvement of the previous work [18].

AB - We study the large time asymptotics of solutions to the Cauchy problem for the modified Korteweg-de Vries equation (Formula presented) We develop the factorization technique to obtain the large time asymptotics of solutions in the neighborhood of the self-similar solution in the case of nonzero total mass initial data. Our result is an improvement of the previous work [18].

KW - Large time asymptotics

KW - Modified Korteweg-de Vries equation

KW - Self-similar solution

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M3 - Article

AN - SCOPUS:85010284766

VL - 52

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EP - 95

JO - SUT Journal of Mathematics

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