Soliton solutions of an integrable nonlocal modified Korteweg–de Vries equation through inverse scattering transform

It is well known that the nonlinear Schrödinger (NLS) equation is a very important integrable equation. Ablowitz and Musslimani introduced and investigated an integrable nonlocal NLS equation through inverse scattering transform. Very recently, we proposed an integrable nonlocal modified Korteweg–de...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 453; no. 2; pp. 973 - 984
Main Authors Ji, Jia-Liang, Zhu, Zuo-Nong
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.09.2017
Subjects
Inverse scattering transform
Nonlocal modified KdV equation
Soliton solution
Inverse scattering transform
Soliton solution
Nonlocal modified KdV equation
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Summary:It is well known that the nonlinear Schrödinger (NLS) equation is a very important integrable equation. Ablowitz and Musslimani introduced and investigated an integrable nonlocal NLS equation through inverse scattering transform. Very recently, we proposed an integrable nonlocal modified Korteweg–de Vries equation (mKdV) which can also be found in the papers of Ablowitz and Musslimani. We have constructed the Darboux transformation and soliton solutions for the nonlocal mKdV equation. In this paper, we will investigate further the nonlocal mKdV equation. We will give its exact solutions including soliton and breather through inverse scattering transformation. These solutions have some new properties, which are different from the ones of the mKdV equation.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2017.04.042