تقرير
On Rational Solutions of Dressing Chains of Even Periodicity
| العنوان: | On Rational Solutions of Dressing Chains of Even Periodicity |
|---|---|
| المؤلفون: | Aratyn, H., Gomes, J. F., Lobo, G. V., Zimerman, A. H. |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics Mathematical Physics Nonlinear Sciences |
| مصطلحات موضوعية: | Nonlinear Sciences - Exactly Solvable and Integrable Systems, Mathematical Physics, 33E17, 34M55 |
| الوصف: | We develop a systematic approach to deriving rational solutions and obtaining classification of their parameters for dressing chains of even N periodicity or equivalently $A^{(1)}_{N-1}$ invariant Painlev\'e equations. This construction identifies rational solutions with points on orbits of fundamental shift operators acting on first-order polynomial solutions derived for dressing chains of even periodicity. We also obtain conditions for the existence of special function solutions that occur for a special class of first-order polynomial solutions. For the special case of the N=4 dressing chain equations the method yields all the known rational solutions of Painlev\'e V equation. They are obtained through action of shift operators on the two independent first-order polynomial solutions. The formalism naturally extends to N=6 and beyond as shown in the paper. Comment: 29 pages |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.3390/sym15010249 |
| URL الوصول: | http://arxiv.org/abs/2206.06482 |
| رقم الأكسشن: | edsarx.2206.06482 |
| قاعدة البيانات: | arXiv |
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