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Variational approximations of soliton dynamics in the Ablowitz-Musslimani nonlinear Schrödinger equation

Rusin, R and Kusdiantara, R and Susanto, H (2019) 'Variational approximations of soliton dynamics in the Ablowitz-Musslimani nonlinear Schrödinger equation.' Physics Letters A. ISSN 0375-9601

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Abstract

We study the integrable nonlocal nonlinear Schrödinger equation proposed by Ablowitz and Musslimani, that is considered as a particular example of equations with parity-time (PT) symmetric self-induced potential. We consider dynamics (including collisions) of moving solitons. Analytically we develop a collective coordinate approach based on variational methods and examine its applicability in the system. We show numerically that a single moving soliton can pass the origin and decay or be trapped at the origin and blows up at a finite time. Using a standard soliton ansatz, the variational approximation can capture the dynamics well, including the finite-time blow up, even though the ansatz is relatively far from the actual blowing-up soliton solution. In the case of two solitons moving towards each other, we show that there can be a mass transfer between them, in addition to wave scattering. We also demonstrate that defocussing nonlinearity can support bright solitons.

Item Type: Article
Uncontrolled Keywords: Integrable nonlocal nonlinear Schrödinger equation, Variational methods, Dynamics of moving solitons, Collisions
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health > Mathematical Sciences, Department of
Depositing User: Elements
Date Deposited: 05 Apr 2019 08:41
Last Modified: 05 Apr 2019 08:41
URI: http://repository.essex.ac.uk/id/eprint/24416

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