Feng, Bao-Feng; Maruno, Ken-Ichi; Ohta, Yasuhiro Integrable discretizations of the short pulse equation. (English) Zbl 1189.78051 J. Phys. A, Math. Theor. 43, No. 8, Article ID 085203, 14 p. (2010). Authors’ abstract: We propose integrable semi-discrete and full-discrete analogues of the short pulse (SP) equation. The key construction is the bilinear form and determinant structure of solutions of the SP equation. We also give the determinant formulas of \(N\)-soliton solutions of the semi-discrete and full-discrete analogues of the SP equations, from which the multi-loop and multi-breather solutions can be generated. In the continuous limit, the full-discrete SP equation converges to the semi-discrete SP equation, and then to the continuous SP equation. Based on the semi-discrete SP equation, an integrable numerical scheme, i.e. a self-adaptive moving mesh scheme, is proposed and used for the numerical computation of the short pulse equation. Reviewer: Aleksander Pankov (Baltimore) Cited in 1 ReviewCited in 53 Documents MSC: 78A60 Lasers, masers, optical bistability, nonlinear optics Keywords:short pulse equation; integrable discretization; solitons Software:PSEUDO PDFBibTeX XMLCite \textit{B.-F. Feng} et al., J. Phys. A, Math. Theor. 43, No. 8, Article ID 085203, 14 p. (2010; Zbl 1189.78051) Full Text: DOI arXiv