2009/12/10 by Bao-Feng Feng, Ken-ichi Maruno, Yasuhiro Ohta · 1 citation
Physics and Astronomy · Mathematics · #nlin.SI #math-ph #math.MP #nlin.PS
paper · pdf · doi:10.1088/1751-8113/43/8/085203
published as Journal of Physics A: Mathematical and Theoretical, 43 (2010) 085203 · 15 pages
arxiv created 2009/12/10 · arxiv updated 2011/05/10
In the present paper, we propose integrable semi-discrete and full-discrete analogues of the short pulse (SP) equation. The key of the construction is the bilinear forms 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, 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.