تقرير
On trilinear and quadrilinear equations associated with the lattice Gel'fand-Dikii hierarchy
| العنوان: | On trilinear and quadrilinear equations associated with the lattice Gel'fand-Dikii hierarchy |
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| المؤلفون: | van der Kamp, P. H., Nijhoff, F. W., McLaren, D. I., Quispel, G. R. W |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics Mathematical Physics Nonlinear Sciences |
| مصطلحات موضوعية: | Nonlinear Sciences - Exactly Solvable and Integrable Systems, Mathematical Physics, Mathematics - Combinatorics |
| الوصف: | Introduced in 2012, by Zhang, Zhao, and Nijhoff, the trilinear Boussinesq equation is the natural form of the equation for the $\tau$-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. Comment: 13 pages, 5 figures, Submitted to a special issue devoted to the celebration of 120 years from the day of birth of the famous Soviet mathematician A. Kolmogorov |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2407.11175 |
| رقم الأكسشن: | edsarx.2407.11175 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |