Analytical and numerical studies for integrable and non-integrable fractional discrete modified Korteweg-de Vries hierarchies
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866914688116195328 |
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| author | Liu, Qin-Ling Guo, Rui Huang, Ya-Hui Li, Xin |
| author_facet | Liu, Qin-Ling Guo, Rui Huang, Ya-Hui Li, Xin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_13872 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Analytical and numerical studies for integrable and non-integrable fractional discrete modified Korteweg-de Vries hierarchies Liu, Qin-Ling Guo, Rui Huang, Ya-Hui Li, Xin Exactly Solvable and Integrable Systems Mathematical Physics 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. |
| title | Analytical and numerical studies for integrable and non-integrable fractional discrete modified Korteweg-de Vries hierarchies |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics |
| url | https://arxiv.org/abs/2402.13872 |