scholarly journals On properties of meromorphic solutions for difference Painlevé equations

2015 ◽  
Vol 2015 (1) ◽  
Author(s):  
Chang-Wen Peng ◽  
Zong-Xuan Chen
Keyword(s):  
Painlevé Equations ◽  
Meromorphic Solutions ◽  
Painleve Equations

scholarly journals The properties of solutions for several types of Painlevé equations concerning fixed-points, zeros and poles

2019 ◽  
Vol 17 (1) ◽  
pp. 1014-1024
Author(s):  
Hong Yan Xu ◽  
Xiu Min Zheng
Keyword(s):  
Fixed Points ◽  
Difference Equations ◽  
Painlevé Equations ◽  
Meromorphic Solutions ◽  
Painleve Equations ◽  
Zeros And Poles

Abstract The purpose of this manuscript is to study some properties on meromorphic solutions for several types of q-difference equations. Some exponents of convergence of zeros, poles and fixed points related to meromorphic solutions for some q-difference equations are obtained. Our theorems are some extension and improvements to those results given by Qi, Peng, Chen, and Zhang.

scholarly journals Zeros, Poles, and Fixed Points of Meromorphic Solutions of Difference Painlevé Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Shuang-Ting Lan ◽  
Zong-Xuan Chen
Keyword(s):  
Fixed Points ◽  
Painlevé Equations ◽  
Meromorphic Solutions ◽  
Painleve Equations

In this paper, we mainly study the properties of transcendental meromorphic solutionsf(z)of difference Painlevé equationsw(z+1)w(z-1)(w(z)-1)=η(z)w2(z)-λ(z)w(z)andw(z+1)w(z-1)(w(z)-1)=η(z)w(z)and obtain precise estimations of the exponents of convergence of zeros, poles ofΔf(z)andΔf(z)/f(z), and of fixed points off(z+c)for anyc∈ℂ.

scholarly journals BPS Quivers of Five-Dimensional SCFTs, Topological Strings and q-Painlevé Equations

2021 ◽  
Author(s):  
Giulio Bonelli ◽  
Fabrizio Del Monte ◽  
Alessandro Tanzini
Keyword(s):  
Topological String ◽  
Cluster Algebra ◽  
Painlevé Equations ◽  
Partition Functions ◽  
Quantum Field Theories ◽  
Particle Spectrum ◽  
Yang Mills ◽  
Painleve Equations ◽  
Rank One ◽  
Bilinear Equations

AbstractWe study the discrete flows generated by the symmetry group of the BPS quivers for Calabi–Yau geometries describing five-dimensional superconformal quantum field theories on a circle. These flows naturally describe the BPS particle spectrum of such theories and at the same time generate bilinear equations of q-difference type which, in the rank one case, are q-Painlevé equations. The solutions of these equations are shown to be given by grand canonical topological string partition functions which we identify with $$\tau $$ τ -functions of the cluster algebra associated to the quiver. We exemplify our construction in the case corresponding to five-dimensional SU(2) pure super Yang–Mills and $$N_f=2$$ N f = 2 on a circle.

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