A Method of Solution for Painleve Equations: Painleve IV, V,

Abstract

A method to solve the initial value problem associated with the Painleve equations IV, V is given. The procedure involves formulating a Riemann-Hilbert boundary value problem on intersecting lines for the inverse monodromy problem. The boundary value problem is reduced to a sequence of standard problems on single lines in a certain range of parameter squares. Schlesinger transformations allow one to completely cover the parameter space. Special solutions are constructed from special cases of the Riemann problem as well.

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1987
Accession Number
ADA193270

Entities

People

  • A. S. Fokas
  • M. J. Ablowitz
  • U. Mugan

Organizations

  • Clarkson University

Tags

Communities of Interest

  • Air Platforms
  • C4I

DTIC Thesaurus Topics

  • Analytic Functions
  • Asymptotic Series
  • Boundary Value Problems
  • Cauchy Problem
  • Differential Equations
  • Discontinuities
  • Equations
  • Formulas (Mathematics)
  • Integral Equations
  • Integrals
  • Inverse Problems
  • Inverse Scattering
  • Linear Systems
  • Meromorphic Functions
  • New York
  • Rational Functions
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Linear Algebra

Technology Areas

  • Space