Integrable semi-discretizations of 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.

arXiv commentJ. Phys. A: Mathematical and Theoretical, to be published

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Cited by in corpus (5)

• Generalizations of the short pulse equation
• Discontinuous Galerkin methods for the Ostrovsky-Vakhnenko equation
• Integrable discretization of recursion operators and unified bilinear forms to soliton hierarchies
• Linear instability and uniqueness of the peaked periodic wave in the reduced Ostrovsky equation
• Multi-soliton solution to the two-component Hunter-Saxton equation