Analytical and numerical studies for integrable and non-integrable fractional discrete modified Korteweg-de Vries hierarchies
Abstract
Under investigation in this paper is the fractional integrable and non-integrable discrete modified Korteweg-de Vries hierarchies. The linear dispersion relations, completeness relations, inverse scattering transform, and fractional soliton solutions of the fractional integrable discrete modified Korteweg-de Vries hierarchy will be explored. The inverse scattering problem will be solved accurately by using Gel'fand-Levitan-Marchenko (GLM) equations and Riemann-Hilbert (RH) problem. The peak velocity of fractional soliton solutions will be analyzed. The numerical solutions of the non-integrable fractional averaged discrete modified Korteweg-de Vries equation which has a simpler form than the integrable one will be obtained by a split-step fourier method.
Keywords
Cite
@article{arxiv.2402.13872,
title = {Analytical and numerical studies for integrable and non-integrable fractional discrete modified Korteweg-de Vries hierarchies},
author = {Qin-Ling Liu and Rui Guo and Ya-Hui Huang and Xin Li},
journal= {arXiv preprint arXiv:2402.13872},
year = {2024}
}