Investigation of Painlevé property under time singularities transformations

DOI10.1063/1.529593zbMath0760.34010OpenAlexW1989292718MaRDI QIDQ4032264

Alain Goriely

Publication date: 1 April 1993

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.529593

zbMATH Keywords

Painlevé propertyfirst integralsPainlevé testcoordinate transformations in the complex planenegative resonancessingularities structureweak Painlevé conjecture

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)

Related Items (12)

Jordan Manifolds and Dispersionless KdV Equations ⋮ The singularity analysis for nearly integrable systems: homoclinic intersections and local multivaluedness ⋮ Singularity analysis in planar vector fields ⋮ Reciprocal transformations, Painlevé property and solutions of energy-dependent Schrödinger hierarchies. ⋮ Finite-time blow-up in dynamical systems ⋮ Weak-Painlevé property and integrability of general dynamical systems ⋮ Necessary and sufficient conditions for finite time singularities in ordinary differential equations ⋮ Unbounded trajectories of dynamical systems. ⋮ Symbolic computation of the Painlevé test for nonlinear partial differential equations using Maple ⋮ Hamiltonian structure and Darboux theorem for families of generalized Lotka–Volterra systems ⋮ Graph-theoretic description of the interplay between non-linearity and connectivity in biological systems ⋮ Algebraic decoupling of variables for systems of ODEs of quasipolynomial form

Cites Work

• Integrals of quadratic ordinary differential equations in \(\mathbb R^3\): the Lotka-Volterra system
• Painlevé property and geometry
• Branching of solutions and the nonexistence of first integrals in Hamiltonian mechanics. II
• Hamiltonians with high-order integrals and the ‘‘weak-Painlevé’’ concept
• The weak-Painlevé property as a criterion for the integrability of dynamical systems
• A connection between nonlinear evolution equations and ordinary differential equations of P-type. I
• Analytical approach to initial-value problems in nonlinear systems
• Existence of stable orbits in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="italic">x</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="italic">y</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>potential
• Discrete versions of the Painlevé equations
• Necessary condition for the existence of algebraic first integrals

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