Discretising the Painlevé equations à la Hirota-Mickens
From MaRDI portal
Publication:2861687
DOI10.1063/1.3682240zbMath1274.34261OpenAlexW2014547044MaRDI QIDQ2861687
Ralph Willox, Junkichi Satsuma, Alfred Ramani, Basile Grammaticos
Publication date: 11 November 2013
Published in: Journal of Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1063/1.3682240
Weyl theory and its generalizations for ordinary differential equations (34B20) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55)
Related Items (9)
On a novel representation of discrete Painlevé equations ⋮ Modeling Cooperation and Competition in Biological Communities ⋮ Multiplicative equations related to the affine Weyl group E8 ⋮ A systematic method for constructing discrete Painlevé equations in the degeneration cascade of the E8 group ⋮ On the limits of discrete Painlevé equations associated with the affine Weyl group E8 ⋮ Revisiting the human and nature dynamics model ⋮ Modelling the Effect of Virulent Variants with SIR ⋮ A new family of discrete Painlevé equations and associated linearisable systems ⋮ On the canonical forms of QRT mappings and discrete Painlevé equations
Cites Work
- Discretising systematically the Painlevé equations
- Integrable mappings with transcendental invariants
- On the \(\tau \)-function of the Painlevé equations
- From continuous to discrete Painlevé equations
- Rational surfaces associated with affine root systems and geometry of the Painlevé equations
- The hunting for the discrete Painlevé equations
- Integrable mappings and soliton equations. II
- A differential equation for orthogonal polynomials
- Discretization of the Euler Top
- An affine Weyl group approach to the eight-parameter discrete Painlevé equation
- Linearizable QRT mappings
- Exact solutions to a finite-difference model of a nonlinear reaction-advection equation: Implications for numerical analysis
- How to discretize differential systems in a systematic way
- On Integrability of Hirota–Kimura-Type Discretizations: Experimental Study of the Discrete Clebsch System
- From continuous Painlevé IV to the asymmetric discrete Painlevé I
- From the continuous PV to discrete Painlev$eacute$ equations
- Discrete versions of the Painlevé equations
- Do integrable mappings have the Painlevé property?
- Discrete integrable systems from continuous Painlevé equations through limiting procedures
- Growth and integrability in discrete systems
- Advances in the Applications of Nonstandard Finite Difference Schemes
- Asymmetric discrete Painlevé equations
- On the autonomous limit of discrete Painlevé equations
This page was built for publication: Discretising the Painlevé equations à la Hirota-Mickens
