Open Access
June 2016 Factorization technique for the modified Korteweg-de Vries equation
Nakao Hayashi, Pavel I. Naumkin
Author Affiliations +
SUT J. Math. 52(1): 49-95 (June 2016). DOI: 10.55937/sut/1469055608

Abstract

We study the large time asymptotics of solutions to the Cauchy problem for the modified Korteweg-de Vries equation

tu13x3u=x(u3), t>0,xR,u(0,x)=u0(x), xR.

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].

Funding Statement

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.

Acknowledgments

We are grateful to an unknown referee for many useful suggestions and comments and letting us know the recent papers [9] and [11].

Citation

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Nakao Hayashi. Pavel I. Naumkin. "Factorization technique for the modified Korteweg-de Vries equation." SUT J. Math. 52 (1) 49 - 95, June 2016. https://doi.org/10.55937/sut/1469055608

Information

Received: 9 February 2016; Revised: 2 May 2016; Published: June 2016
First available in Project Euclid: 8 June 2022

Digital Object Identifier: 10.55937/sut/1469055608

Subjects:
Primary: 35Q35 , 81Q05

Keywords: large time asymptotics , Modified Korteweg-de Vries equation , self-similar solution

Rights: Copyright © 2016 Tokyo University of Science

Vol.52 • No. 1 • June 2016
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