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Abstract: In the present paper, we propose integrable semi-discrete and full-discreteanalogues of the short pulse SP equation. The key of the construction is thebilinear forms and determinant structure of solutions of the SP equation. Wealso give the determinant formulas of N-soliton solutions of the semi-discreteand full-discrete analogues of the SP equations, from which the multi-loop andmulti-breather solutions can be generated. In the continuous limit, thefull-discrete SP equation converges to the semi-discrete SP equation, then tothe continuous SP equation. Based on the semi-discrete SP equation, anintegrable numerical scheme, i.e., a self-adaptive moving mesh scheme, isproposed and used for the numerical computation of the short pulse equation.



Author: Bao-Feng Feng, Ken-ichi Maruno, Yasuhiro Ohta

Source: https://arxiv.org/







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