Hierarchies of q-discrete Painleve equations

مقال فى مجلة

2020

تم النشر فى: https://dx.doi.org/10.1080/14029251.2020.1757235

In this paper, we construct a new hierarchy based on the third q-discrete Painleve ́ equation (qPIII) and also study the hierarchy of the second q-discrete Painleve ́ equation (qPII). Both hierarchies are derived by using reductions of the general lattice modified Korteweg-de Vries equation. Our results include Lax pairs for both hierarchies and these turn out to be higher degree expansions of the non-resonant ones found by Joshi and Nakazono [29] for the second-order cases. We also obtain Ba ̈cklund transformations for these hierarchies. Special q-rational solutions of the hierarchies are constructed and corresponding q-gamma functions that solve the associated linear problems are derived.

• نوع عمل المنشور: جزء من رسالة الدكتوراه
• رقم المجلد: 27
• رقم الانشاء: 3
• مجلة/صحيفة: Journal of Nonlinear Mathematics Physics
• الصفحات: 453-477