Integrable semi-discretization of a multi-component short pulse equation

Abstract

In the present paper, we mainly study the integrable semi-discretization of a multi-component short pulse equation. Firstly, we briefly review the bilinear equations for a multi-component short pulse equation proposed by Matsuno (J. Math. Phys. \textbf{52} 123705) and reaffirm its $N$-soliton solution in terms of pfaffians. Then by using a Bäcklund transformation of the bilinear equations and defining a discrete hodograph (reciprocal) transformation, an integrable semi-discrete multi-component short pulse equation is constructed. Meanwhile, its $N$-soliton solution in terms of pfaffians is also proved.

arXiv commentJ. Math. Phys., to appear, 22 pages, 2 figures

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• An integrable semi-discrete Degasperis-Procesi equation
• Integrable semi-discretization of complex and multi-component coupled dispersionless systems and their solutions