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New complex-valued solutions of Painlevé IV: An application to the nonlinear Schrödinger equation

Yemm, LT and Bassom, A ORCID: 0000-0003-3275-7801 2019 , 'New complex-valued solutions of Painlevé IV: An application to the nonlinear Schrödinger equation' , Applied Mathematics Letters, vol. 101 , pp. 1-7 , doi: 10.1016/j.aml.2019.106060.

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Abstract

This paper is devoted to identifying some novel complex-valued solutions of the fourth Painlevé equation (PIV). This equation possesses two parameters and past work has identified many exact solutions of PIV for certain real values of this pair of constants. Two hierarchies of solutions are obtained that are distinguished by the fact that the associated parameters are complex valued. These solutions are applied to the nonlinear Schrödinger equation which enables a new similarity solution to be derived.

Item Type: Article
Authors/Creators:Yemm, LT and Bassom, A
Keywords: Painleve IV, Backlund transformation, nonlinear Schrodinger equation, symmetry solutions
Journal or Publication Title: Applied Mathematics Letters
Publisher: Pergamon-Elsevier Science Ltd
ISSN: 0893-9659
DOI / ID Number: 10.1016/j.aml.2019.106060
Copyright Information:

Copyright 2019 Elsevier Ltd.

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