Annals of Mathematical Sciences and Applications

Volume 2 (2017)

Number 2

Guest Editors: Tai-Chia Lin (National Taiwan University), Wen-Wei Lin (National Chiao Tung University), Tony Wen-Hann Sheu (National Taiwan University), Weichung Wang (National Taiwan University), Chih-wen Weng (National Chiao Tung University), and Salil Vadhan (Harvard University).

Reverse space and time nonlocal coupled dispersionless equation and its solutions

Pages: 409 – 429

DOI: https://dx.doi.org/10.4310/AMSA.2017.v2.n2.a8

Authors

Jialiang Ji (School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, China)

Zhelin Huang (School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, China)

Zuonong Zhu (School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, China)

Abstract

Coupled dispersionless (CD) equation is an important integrable model since it describes the current-fed string in a certain external magnetic field. Recently, Ablowitz and Musslimani introduced a class of reverse space, reverse time and reverse space and time nonlocal integrable equations, including nonlocal nonlinear Schrödinger equation, nonlocal sine-Gordon equation and nonlocal Davey–Stewartson equation etc. In this paper we study an integrable reverse space and time nonlocal CD equation. By applying the Darboux transformation, we present the one-soliton and two-soliton solutions for the nonlocal CD equation. We also show the asymptotic analysis of the one-soliton solution from nonzero seed and two-soliton solutions.

Keywords

nonlocal coupled dispersionless equation, Darboux transformation, soliton solutions

Full Text (PDF format)

Received 14 March 2017

Published 10 August 2017