Annals of Mathematical Sciences and Applications
Volume 2 (2017)
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
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.
nonlocal coupled dispersionless equation, Darboux transformation, soliton solutions
Received 14 March 2017
Published 10 August 2017