A study on the fourth q-Painlevé equation

Abstract

A q-difference analogue of the fourth Painlevé equation is proposed. Its symmetry structure and some particular solutions are investigated.

18 pages

Cited by in corpus (42)

• Geometric Aspects of Painlevé Equations
• q-Difference equations of KdV type and "Chazy-type" second-degree difference equations
• Hypergeometric solutions to the q-Painlevé equation of type $A_4^{(1)}$
• On a q-difference Painlevé III equation: I. Derivation, symmetry and Riccati type solutions
• q-Painlevé systems arising from q-KP hierarchy
• Hypergeometric $\tau$-Functions of the $q$-Painlevé System of Type $E_7^{(1)}$
• On a q-difference Painlevé III equation: II. Rational solutions
• Projective reduction of the discrete Painlevé system of type $(A_2+A_1{)}^{(1)}$
• Tropical Robinson-Schensted-Knuth correspondence and birational Weyl group actions
• Quantum Painlevé systems of type $A_l^{(1)}$
• Lattice equations arising from discrete Painlevé systems (I): $(A_2+A_1{)}^{(1)}$ and $(A_1+A_1^{\prime }{)}^{(1)}$ cases
• Lax pairs of discrete Painlevé equations: $(A_2+A_1{)}^{(1)}$ case
• Hypergeometric Solutions for the $q$-Painlevé Equation of type $E_6^{(1)}$ by Padé Method
• Affine Weyl group approach to Painlevé equations
• Universal character and q-difference Painlevé equations with affine Weyl groups
• Symmetries and Special Solutions of Reductions of the Lattice Potential KdV Equation
• Invariant varieties of periodic points for some higher dimensional integrable maps
• Hypergeometric $\tau$ Function of the $q$-Painlevé Systems of Type $(A_2+A_1{)}^{(1)}$
• The Padé interpolation method applied to $q$-Painlevé equations
• Desargues maps and their reductions
• Hypergeometric solutions to the q-Painlevé equations
• Quantum groups and quantization of Weyl group symmetries of Painlevé systems
• The Padé interpolation method applied to $q$-Painlevé equations II (differential grid version)
• From Polygons to Ultradiscrete Painlevé Equations
• Regularity of quantum tau-functions generated by quantum birational Weyl group actions
• Full-parameter discrete Painlevé systems from non-translational Cremona isometries
• On the Rational Solutions of q-Painlevé V Equation
• Hypergeometric $\tau$ Functions of the $q$-Painlevé Systems of Types $A_4^{(1)}$ and $(A_1+A_1^{\prime }{)}^{(1)}$
• Quantizing the discrete Painlevé VI equation : The Lax formalism
• Discrete Painlevé transcendent solutions to the multiplicative type discrete KdV equations
• On the recurrence coefficients for the $q$-Laguerre weight and discrete Painlevé equations
• Quantizing the Bäcklund transformations of Painlevé equations and the quantum discrete Painlevé VI equation
• Discrete dynamical systems with $W(A_{m-1}^{(1)}\times A_{n-1}^{(1)})$ symmetry
• Reflection groups and discrete integrable systems
• Symmetries in Connection Preserving Deformations
• On symmetric solutions of the fourth $q$-Painlevé equation
• Hypergeometric Solutions of the $A_4^{(1)}$-Surface $q$-Painlevé IV Equation
• Construction of Hypergeometric Solutions to the q-Painlevé Equations
• The extended Weyl group $\tilde{W}(D_5^{(1)})$ as an extension of KNY's birational representation of $\tilde{W}(A_1^{(1)}\times A_3^{(1)})$
• $q$-deformation of random partitions, determinantal structure, and Riemann-Hilbert problem
• Nambu-Hamiltonian flows associated with discrete maps
• An ultradiscrete matrix version of the fourth Painleve equation