Integrable discretizations of the short pulse equation

Details Integrable discretizations of the short pulse equation Integrable discretizations of the short pulse equation

2009-12-10

arxiv.org/abs/0912.1914v1

Journal of Physics A: Mathematical and Theoretical, 43 (2010) 085203

Nonlinear Sciences

Exactly Solvable and Integrable Systems

15 pages

Scientific paper

10.1088/1751-8113/43/8/085203

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.

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