标题： 可积与不可积分数离散修改Korteweg-de Vries层次的分析与数值研究 显示英文标题

标题： Analytical and numerical studies for integrable and non-integrable fractional discrete modified Korteweg-de Vries hierarchies

摘要： 本文研究的是分数阶可积与不可积离散改进Korteweg-de Vries层次结构。 将探讨分数阶可积离散改进Korteweg-de Vries层次结构的线性色散关系、完备性关系、逆散射变换和分数阶孤子解。 将通过Gel'fand-Levitan-Marchenko（GLM）方程和Riemann-Hilbert（RH）问题准确求解逆散射问题。 将分析分数阶孤子解的峰值速度。 将通过分裂步傅里叶方法获得具有比可积形式更简单形式的不可积分数阶平均离散改进Korteweg-de Vries方程的数值解。 显示英文摘要

摘要： 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.