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arXiv · 1905.09112

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

Rahmi Rusin·Rudy Kusdiantara·Hadi Susanto
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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 ($\mathcal{PT}$) 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 defocusing nonlinearity can support bright solitons.

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Rahmi Rusin, Rudy Kusdiantara, Hadi Susanto. 2019-05-22. Variational approximations of soliton dynamics in the Ablowitz-Musslimani nonlinear Schrödinger equation. https://doi.org/10.1016/j.physleta.2019.03.043

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