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Hirota’s Method and the Painlevé Property

  • J. D. Gibbon
  • M. Tabor
Conference paper
Part of the Springer Series in Synergetics book series (SSSYN, volume 30)

Abstract

Given a system of nonlinear ordinary or partial differential equations a most challenging problem is to find an analytical test to determine whether the given system is integrable. In the case of systems of o.d.e’s integrability (in the classical sense of “integration by quadratures” [1]) requires one to find as many integrals of the motion as the order of the system. However, in the case of Hamiltonian systems, owing to the special symplectic structure of phase space, a complete integration can be effected by the identification of as many involutive integrals as there are degrees of freedom (N). For integrable Hamiltonian systems the flow is confined to N-dimensional tori embedded in the 2N-dimensional phase space.

Keywords

Integrable Hamiltonian System Schwarzian Derivative Toda Chain Inverse Scattering Transform Singular Manifold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • J. D. Gibbon
    • 1
  • M. Tabor
    • 2
  1. 1.Department of MathematicsImperial CollegeLondonGreat Britain
  2. 2.Department of Applied Physics & Nuclear EngineeringColumbia UniversityNew YorkUSA

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