Integrable full discretization of the multi-component short pulse equation

2026/07/06 by Ayako Hori, Yuta Tanaka, Ken-ichi Maruno +2 · 1 voice
Physics and Astronomy · #nlin.SI #math-ph

paper · pdf

Abstract

We propose a new formulation of the multi-component short pulse (MCSP) equation that includes the coupled complex short pulse (CCSP) equation as a reduction. Using Hirota's bilinear method, we construct its N-soliton solutions in Pfaffian form. We then derive integrable semi-discrete and fully discrete analogues of the MCSP equation admitting Pfaffian N-soliton solutions. The resulting fully discrete system provides a practical self-adaptive moving mesh scheme for numerical simulations. For the parameter sets considered, numerical simulations demonstrate excellent agreement between the numerical and exact solutions, confirming the robustness and high accuracy of the proposed scheme.

Citations

• An integrable semi-discrete Degasperis-Procesi equation
• Integrable discretizations and self-adaptive moving mesh method for a coupled short pulse equation
• Integrable semi-discretization of a multi-component short pulse equation
• Integrable semi-discretizations of the reduced Ostrovsky equation
• Self-adaptive moving mesh schemes for short pulse type equations and their Lax pairs
• Complex short pulse and coupled complex short pulse equations
• Integrable discretizations of the Dym equation
• A novel multi-component generalization of the short pulse equation and its multisoliton solutions
• Discrete Integrable Systems and Hodograph Transformations Arising from Motions of Discrete Plane Curves
• Integrable discretizations for the short wave model of the Camassa-Holm equation
• Integrable discretizations of the short pulse equation
• A self-adaptive mesh method for the Camassa-Holm equation
• An integrable semi-discretization of the Camassa-Holm equation and its determinant solution
• The Short Pulse Equation Is Integrable
• Propagation of ultra-short optical pulses in cubic nonlinear media
• Ultra-short pulses in linear and nonlinear media

Discussions

• Ayako Hori, Yuta Tanaka, Ken-ichi Maruno, Yasuhiro Ohta, Bao-Feng Feng: Integrable full discretization of the multi-component short pulse equation https://arxiv.org/abs/2607.04756 https://arxiv.org/pd [bsky, 0 points, 0 comments]

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