تقرير
Integrable quadratic structures in peakon models
| العنوان: | Integrable quadratic structures in peakon models |
|---|---|
| المؤلفون: | Avan, J., Frappat, L., Ragoucy, E. |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics Mathematical Physics Nonlinear Sciences |
| مصطلحات موضوعية: | Nonlinear Sciences - Exactly Solvable and Integrable Systems, Mathematical Physics |
| الوصف: | We propose realizations of the Poisson structures for the Lax representations of three integrable $n$-body peakon equations, Camassa--Holm, Degasperis--Procesi and Novikov. The Poisson structures derived from the integrability structures of the continuous equations yield quadratic forms for the $r$-matrix representation, with the Toda molecule classical $r$-matrix playing a prominent role. We look for a linear form for the $r$-matrix representation. Aside from the Camassa--Holm case, where the structure is already known, the two other cases do not allow such a presentation, with the noticeable exception of the Novikov model at $n=2$. Generalized Hamiltonians obtained from the canonical Sklyanin trace formula for quadratic structures are derived in the three cases. Comment: 19 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2203.13593 |
| رقم الأكسشن: | edsarx.2203.13593 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |