On trilinear and quadrilinear equations associated with the lattice Gel’fand–Dikii hierarchy
Introduced in Zhang et al. (2012), the trilinear Boussinesq equation is the natural form of the equation for the τ-function of the lattice Boussinesq system. In this paper we study various aspects of this equation: its highly nontrivial derivation from the bilinear lattice AKP equation under dimensi...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2024-12-01
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| Series: | Partial Differential Equations in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818124002997 |
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| Summary: | Introduced in Zhang et al. (2012), the trilinear Boussinesq equation is the natural form of the equation for the τ-function of the lattice Boussinesq system. In this paper we study various aspects of this equation: its highly nontrivial derivation from the bilinear lattice AKP equation under dimensional reduction, a quadrilinear dual lattice equation, conservation laws, and periodic reductions leading to higher-dimensional integrable maps and their Laurent property. Furthermore, we consider a higher Gel’fand–Dikii lattice system, its periodic reductions and Laurent property. As a special application, from both a trilinear Boussinesq recurrence as well as a higher Gel’fand–Dikii system of three bilinear recurrences, we establish Somos-like integer sequences. |
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| ISSN: | 2666-8181 |