Rusin, R and Kusdiantara, R and Susanto, H (2019) 'Variational approximations of soliton dynamics in the Ablowitz-Musslimani nonlinear Schrödinger equation.' Physics Letters A, 383 (17). pp. 2039-2045. 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 |
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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 Faculty of Science and Health > Mathematical Sciences, Department of |
SWORD Depositor: | Elements |
Depositing User: | Elements |
Date Deposited: | 05 Apr 2019 08:41 |
Last Modified: | 06 Jan 2022 13:59 |
URI: | http://repository.essex.ac.uk/id/eprint/24416 |
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