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Numerical studies of the fourth Painlevé equation
journal contribution
posted on 2023-05-18, 18:30 authored by Andrew BassomAndrew Bassom, Clarkson, PA, Hicks, ACIn 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 §→−∞.History
Publication title
IMA Journal of Applied MathematicsVolume
50Pagination
167-193ISSN
0272-4960Department/School
School of Natural SciencesPublisher
Oxford Univ PressPlace of publication
Great Clarendon St, Oxford, England, Ox2 6DpRights statement
Copyright Oxford University Press 1993Repository Status
- Restricted