Painleve Chains for the Study of Integrable Higher Order Differential Equations.

Abstract

A previous paper defines the three fundamental homogeneous active Painleve chains which are generated from the equation u sub 2x = ku sub 2, u sub 2x = ku sub 3, and ux = ku sub 2. This paper shows how the concept of Painleve chains can be extended to Painleve chains generated from hybrid differential equations and the passive differential equation u sub 2 = ku 2 over x. In addition the Schwarzian derivative can be used to generate a Painleve chain with the interesting property of consecutive integral resonances. Finally the 2 x 2 eigenvalue problem of Zakharov and Shabat is shown to generate chains exhibiting some but not all of the features of Painleve chains.

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Document Details

Document Type
Technical Report
Publication Date
Dec 18, 1986
Accession Number
ADA175455

Entities

People

  • R. B. King

Organizations

  • University of Georgia

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algebraic Functions
  • Chemistry
  • Classification
  • Complex Variables
  • Computational Science
  • Differential Equations
  • Eigenvalues
  • Equations
  • Fluid Dynamics
  • Governments
  • Integrals
  • Inverse Scattering
  • Military Research
  • New York
  • Partial Differential Equations
  • Power Series
  • Quadratic Equations

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.
  • Radar Systems Engineering.
  • Wave Propagation and Nonlinear Chaotic Dynamics.