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Integrable full discretization of the multi-component short pulse equation
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.
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BibTeX
@misc{hori2026integrable,
title = {{Integrable full discretization of the multi-component short pulse equation}},
author = {Ayako Hori and Yuta Tanaka and Ken-ichi Maruno and Yasuhiro Ohta and Bao-Feng Feng},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2607.04756},
eprint = {2607.04756},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.04756},
}
RIS
TY - UNPB
TI - Integrable full discretization of the multi-component short pulse equation
AU - Ayako Hori
AU - Yuta Tanaka
AU - Ken-ichi Maruno
AU - Yasuhiro Ohta
AU - Bao-Feng Feng
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2607.04756
UR - https://arxiv.org/abs/2607.04756
AB - 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.
ER -