Bilinear structures of the fourth-order lattice Gel'fand-Dikii equations
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915863664263168 |
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| author | Zhao, Song-lin Wang, Han Zhang, Da-jun |
| author_facet | Zhao, Song-lin Wang, Han Zhang, Da-jun |
| contents | In this paper we derive bilinear forms and present their solutions in Casoratians for several fourth-order lattice Gel'fand-Dikii (lattice GD-4) equations. These equations were recently formulated from the direct linearization approach and exhibit the multidimensionally consistent property in multi-component form. Based on the obtained soliton solutions, we are able to extend these equations by introducing a parameter $δ$. These $δ$-extended lattice GD-4 type equations are still consistent around the cube, and their bilinear forms together with Casoratian solutions are provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_14426 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bilinear structures of the fourth-order lattice Gel'fand-Dikii equations Zhao, Song-lin Wang, Han Zhang, Da-jun Exactly Solvable and Integrable Systems In this paper we derive bilinear forms and present their solutions in Casoratians for several fourth-order lattice Gel'fand-Dikii (lattice GD-4) equations. These equations were recently formulated from the direct linearization approach and exhibit the multidimensionally consistent property in multi-component form. Based on the obtained soliton solutions, we are able to extend these equations by introducing a parameter $δ$. These $δ$-extended lattice GD-4 type equations are still consistent around the cube, and their bilinear forms together with Casoratian solutions are provided. |
| title | Bilinear structures of the fourth-order lattice Gel'fand-Dikii equations |
| topic | Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2510.14426 |