Integrable discretizations and self-adaptive moving mesh method for a coupled short pulse equation. (25th August 2015)

• Record Type: Journal Article
• Authors: Feng, Bao-Feng; Chen, Junchao; Chen, Yong; Maruno, Ken-ichi; Ohta, Yasuhiro
• Is Part Of: Journal of physics. Volume 48:Number 38(2015)
• Publication Date: 2015-08-25
• Subjects: coupled short pulse equation -- integrable discretization -- self-adaptive moving mesh method; 02.30.Ik -- 05.45.Yv -- 42.65.Tg -- 42.81.Dp; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8113/48/38/385202
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: In the present paper, integrable semi-discrete and fully discrete analogues of a coupled short pulse (CSP) equation are constructed. The key to the construction are the bilinear forms and determinant structure of the solutions of the CSP equation. We also construct N -soliton solutions for the semi-discrete and fully discrete analogues of the CSP equations in the form of Casorati determinants. In the continuous limit, we show that the fully discrete CSP equation converges to the semi-discrete CSP equation, then further to the continuous CSP equation. Moreover, the integrable semi-discretization of the CSP equation is used as a self-adaptive moving mesh method for numerical simulations. The numerical results agree with the analytical results very well.