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Numerical studies of the fourth Painlevé equation

Citation

Bassom, AP and Clarkson, PA and Hicks, AC, Numerical studies of the fourth Painleve equation, IMA Journal of Applied Mathematics, 50, (2) pp. 167-193. ISSN 0272-4960 (1993) [Refereed Article]

Copyright Statement

Copyright Oxford University Press 1993

DOI: doi:10.1093/imamat/50.2.167

Abstract

In this paper the authors investigate numerically solutions of a special case of the fourth Painlevé equation given by

d2η/dξ2 = 3η5 + 2ξη3 + (1/4ξ2 - ν - 1/2)η

with ν a parameter, satisfying the boundary condition

η(ξ)→0 as ξ→ + ∞.

Equation (1a) arises as a symmetry reduction of the derivative nonlinear Schrödinger (DNLS) equation, which is a completely integrable soliton equation solvable by inverse scattering techniques. Previous results concerned with solutions of (1) are largely restricted to the case when ν is an integer and very little has been proved when ν is a noninteger. Here a numerical approach to describing solutions of (1) for noninteger ν is adopted, and information is obtained characterizing connection formulae which describe how the asymptotic behaviours of solutions as §→+∞ relate to those as §→−∞.

Item Details

Item Type:Refereed Article
Research Division:Mathematical Sciences
Research Group:Applied Mathematics
Research Field:Theoretical and Applied Mechanics
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Mathematical Sciences
Author:Bassom, AP (Professor Andrew Bassom)
ID Code:107975
Year Published:1993
Web of Science® Times Cited:14
Deposited By:Mathematics and Physics
Deposited On:2016-04-01
Last Modified:2016-11-25
Downloads:0

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