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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:453

Article

Ji, Jia-Liang¹  Zhu, Zuo-Nong¹ 

[1] Shanghai Jiao Tong Univ, Sch Math Sci, 800 Dongchuan Rd, Shanghai 200240, Peoples R China

关键词: Nonlocal modified KdV equation;    Inverse scattering transform;    Soliton solution;   

DOI  :  10.1016/j.jmaa.2017.04.042

来源: Elsevier

【 摘 要 】

It is well known that the nonlinear Schrodinger (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. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free