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


Yemm, LT and Bassom, A, New complex-valued solutions of Painleve IV: An application to the nonlinear Schrodinger equation, Applied Mathematics Letters, 101 Article 106060. ISSN 0893-9659 (2020) [Refereed Article]

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Copyright 2019 Elsevier Ltd.

DOI: doi:10.1016/j.aml.2019.106060


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 Details

Item Type:Refereed Article
Keywords:Painleve IV, Backlund transformation, nonlinear Schrodinger equation, symmetry solutions
Research Division:Mathematical Sciences
Research Group:Pure mathematics
Research Field:Ordinary differential equations, difference equations and dynamical systems
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the mathematical sciences
UTAS Author:Yemm, LT (Mr Liam Yemm)
UTAS Author:Bassom, A (Professor Andrew Bassom)
ID Code:135117
Year Published:2020 (online first 2019)
Web of Science® Times Cited:1
Deposited By:Mathematics and Physics
Deposited On:2019-10-01
Last Modified:2020-05-20

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