Integrable semi-discretizations of the reduced Ostrovsky equation

TL;DR

This paper develops integrable semi-discrete models of the reduced Ostrovsky equation, preserving soliton solutions and clarifying the relationship between two different discretization approaches.

Contribution

It introduces two new semi-discrete integrable versions of the reduced Ostrovsky equation based on its two representations, expanding the understanding of its discretizations.

Findings

Two semi-discrete analogues with N-loop soliton solutions

Clarification of the relationship between the two discretizations

Extension of previous work on the reduced Ostrovsky equation

Abstract

Based on our previous work to the reduced Ostrovsky equation (J. Phys. A 45 355203), we construct its integrable semi-discretizations. Since the reduced Ostrovsky equation admits two alternative representations, one is its original form, the other is the differentiation form, or the short wave limit of the Degasperis-Procesi equation, two semi- discrete analogues of the reduced Ostrovsky equation are constructed possessing the same N-loop soliton solution. The relationship between these two versions of semi-discretizations is also clarified.