Integrable semi-discretization of a modified short wave equation

Abstract

In this paper, we are concerned with one of the integrable equations proposed by Hone et al. (2018). We firstly show that it can be derived from the Tzitzeica equation through hodograph or reciprocal transformations and it is linked to the short wave limits of the DP and Novikov equations, respectively, through Miura transformations. Based on the semi-discrete analogue of CKP-Toda hierarchy, we construct the integrable semi-discretization of what we call the modified short wave equation and provide its multi-soliton solution.