Constraints of the D$Δ$KP hierarchy to the semi-discrete AKNS and Burgers hierarchies
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866911499008606208 |
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| author | Liu, Jin Zhang, Da-jun |
| author_facet | Liu, Jin Zhang, Da-jun |
| contents | The paper investigates three eigenfunction constraints of two (2+1)-dimensional differential-difference integrable systems. First, we revisit the known squared eigenfunction symmetry constraint of the differential-difference Kadomtsev-Petviashvili (D$Δ$KP) hierarchy, which gives rise to a semi-discrete Ablowitz-Kaup-Newell-Segur hierarchy. Second, we introduce a linear eigenfunction constraint for the D$Δ$KP system and obtain a combined semi-discrete Burgers (sdBurgers) hierarchy. In the third one, we consider another linear eigenfunction constraint for the modified D$Δ$KP system and obtain the same combined sdBurgers hierarchy. All these constraint results are proved by using recursive algebraic structures of the involved integrable hierarchies generated by their master symmetries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_08301 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Constraints of the D$Δ$KP hierarchy to the semi-discrete AKNS and Burgers hierarchies Liu, Jin Zhang, Da-jun Exactly Solvable and Integrable Systems The paper investigates three eigenfunction constraints of two (2+1)-dimensional differential-difference integrable systems. First, we revisit the known squared eigenfunction symmetry constraint of the differential-difference Kadomtsev-Petviashvili (D$Δ$KP) hierarchy, which gives rise to a semi-discrete Ablowitz-Kaup-Newell-Segur hierarchy. Second, we introduce a linear eigenfunction constraint for the D$Δ$KP system and obtain a combined semi-discrete Burgers (sdBurgers) hierarchy. In the third one, we consider another linear eigenfunction constraint for the modified D$Δ$KP system and obtain the same combined sdBurgers hierarchy. All these constraint results are proved by using recursive algebraic structures of the involved integrable hierarchies generated by their master symmetries. |
| title | Constraints of the D$Δ$KP hierarchy to the semi-discrete AKNS and Burgers hierarchies |
| topic | Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2603.08301 |