Solutions of local and nonlocal discrete complex modified Korteweg-de Vries equations and continuum limits
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911848749596672 |
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| author | Hu, Ya-Nan Shen, Shou-Feng Zhao, Song-lin |
| author_facet | Hu, Ya-Nan Shen, Shou-Feng Zhao, Song-lin |
| contents | Cauchy matrix approach for the discrete Ablowitz-Kaup-Newell-Segur equations is reconsidered, where two `proper' discrete Ablowitz-Kaup-Newell-Segur equations and two `unproper' discrete Ablowitz-Kaup-Newell-Segur equations are derived. The `proper' equations admit local reduction, while the `unproper' equations admit nonlocal reduction. By imposing the local and nonlocal complex reductions on the obtained discrete Ablowitz-Kaup-Newell-Segur equations, two local and nonlocal discrete complex modified Korteweg-de Vries equations are constructed. For the obtained local and nonlocal discrete complex modified Korteweg-de Vries equations, soliton solutions and Jordan-block solutions are presented by solving the determining equation set. The dynamical behaviors of 1-soliton solution are analyzed and illustrated. Continuum limits of the resulting local and nonlocal discrete complex modified Korteweg-de Vries equations are discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_14150 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Solutions of local and nonlocal discrete complex modified Korteweg-de Vries equations and continuum limits Hu, Ya-Nan Shen, Shou-Feng Zhao, Song-lin Exactly Solvable and Integrable Systems Cauchy matrix approach for the discrete Ablowitz-Kaup-Newell-Segur equations is reconsidered, where two `proper' discrete Ablowitz-Kaup-Newell-Segur equations and two `unproper' discrete Ablowitz-Kaup-Newell-Segur equations are derived. The `proper' equations admit local reduction, while the `unproper' equations admit nonlocal reduction. By imposing the local and nonlocal complex reductions on the obtained discrete Ablowitz-Kaup-Newell-Segur equations, two local and nonlocal discrete complex modified Korteweg-de Vries equations are constructed. For the obtained local and nonlocal discrete complex modified Korteweg-de Vries equations, soliton solutions and Jordan-block solutions are presented by solving the determining equation set. The dynamical behaviors of 1-soliton solution are analyzed and illustrated. Continuum limits of the resulting local and nonlocal discrete complex modified Korteweg-de Vries equations are discussed. |
| title | Solutions of local and nonlocal discrete complex modified Korteweg-de Vries equations and continuum limits |
| topic | Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2404.14150 |