The second Painlevé equation, a related nonautonomous semidiscrete equation, and a limit to the first Painlevé equation: scalar and matrix cases

DOI10.1016/j.physd.2018.12.001zbMath1451.37086OpenAlexW2903614945MaRDI QIDQ2215702

Andrew Pickering, Jonathan A. D. Wattis, Pilar Ruiz Gordoa

Publication date: 14 December 2020

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://nottingham-repository.worktribe.com/output/1450292

zbMATH Keywords

integrable systemsasymptotic behaviourHamiltonian formulations of matrix Painlevé equationsmatrix semidiscrete equationssolutions of matrix second Painlevé equation

Mathematics Subject Classification ID

Integrable difference and lattice equations; integrability tests (39A36) Nonautonomous Hamiltonian dynamical systems (Painlevé equations, etc.) (37J65)

Related Items (3)

Solution classes of the matrix second Painlevé hierarchy ⋮ On matrix fourth Painlevé hierarchies ⋮ Integrability and asymptotic behaviour of a differential-difference matrix equation

Uses Software

• Algorithm 432

Cites Work

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• On matrix Painlevé hierarchies
• Bäcklund transformations for a matrix second Painlevé equation
• Integrable evolution equations on associative algebras
• From continuous to discrete Painlevé equations
• Lump solutions to nonlinear partial differential equations via Hirota bilinear forms
• Rational solutions of the Toda lattice equation in Casoratian form
• Auto-Bäcklund transformations for a matrix partial differential equation
• On the Painlevé test for non-abelian equations
• Bäcklund transformation of matrix equations and a discrete matrix first Painlevé equation
• Behaviour of the extended Toda lattice
• Behaviour of the extended modified Volterra lattice-reductions to generalised mKdV and NLS equations
• Behaviour of the extended Volterra lattice
• Diversity of interaction solutions to the \((2+1)\)-dimensional ito equation
• A nonisospectral extension of the Volterra hierarchy to 2+1 dimensions
• New 2+1 dimensional nonisospectral Toda lattice hierarchy
• An algorithm for solving the matrix equationX = FXF^T+S
• On the Solution to the Inverse Problem for the Toda Chain
• Algebraic structure of discrete zero curvature equations and master symmetries of discrete evolution equations
• Algorithm 432 [C2: Solution of the matrix equation AX + XB = C [F4]]

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