Discretization of the Mikhailov model
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917203352223744 |
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| author | Zhao, Song-lin Mu, Xiao-gang Zhang, Da-jun |
| author_facet | Zhao, Song-lin Mu, Xiao-gang Zhang, Da-jun |
| contents | In this paper the Mikhailov model is discretized by means of the Cauchy matrix approach. A pair of discrete Miura transformations are constructed. The discrete Mikhailov model is a coupled system, in which one equation comes from the compatibility of the two Miura transformations, the other is transformed from the discrete negative order Ablowitz-Kaup-Newell-Segur system by using the Miura transformations. Explicit solutions, including solitons and multiple-pole solutions, are presented via two Cauchy matrix schemes respectively, namely, the Ablowitz-Kaup-Newell-Segur type and the Kadomtsev-Petviashvili type. By straight continuum limits, semi-discrete and continuous Mikhailov models together with their Cauchy matrix structures and solutions are recovered. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_09206 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Discretization of the Mikhailov model Zhao, Song-lin Mu, Xiao-gang Zhang, Da-jun Exactly Solvable and Integrable Systems In this paper the Mikhailov model is discretized by means of the Cauchy matrix approach. A pair of discrete Miura transformations are constructed. The discrete Mikhailov model is a coupled system, in which one equation comes from the compatibility of the two Miura transformations, the other is transformed from the discrete negative order Ablowitz-Kaup-Newell-Segur system by using the Miura transformations. Explicit solutions, including solitons and multiple-pole solutions, are presented via two Cauchy matrix schemes respectively, namely, the Ablowitz-Kaup-Newell-Segur type and the Kadomtsev-Petviashvili type. By straight continuum limits, semi-discrete and continuous Mikhailov models together with their Cauchy matrix structures and solutions are recovered. |
| title | Discretization of the Mikhailov model |
| topic | Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2601.09206 |