TY - JOUR

T1 - Variational approximations of soliton dynamics in the Ablowitz-Musslimani nonlinear Schrödinger equation

AU - Rusin, Rahmi

AU - Kusdiantara, Rudy

AU - Susanto, Hadi

N1 - Funding Information:
R.R (Grant Ref. No: S-5405/LPDP.3/2015 ) and R.K (Grant Ref. No: S-34/LPDP.3/2017 ) gratefully acknowledge financial support from Lembaga Pengelolaan Dana Pendidikan (Indonesia Endowment Fund for Education). The authors thank the three reviewers for their comments that improved the quality of the paper.
Publisher Copyright:
© 2019 Elsevier B.V.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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 decays 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.

AB - 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 decays 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.

KW - Collisions

KW - Dynamics of moving solitons

KW - Integrable nonlocal nonlinear Schrödinger equation

KW - Variational methods

UR - http://www.scopus.com/inward/record.url?scp=85064543670&partnerID=8YFLogxK

U2 - 10.1016/j.physleta.2019.03.043

DO - 10.1016/j.physleta.2019.03.043

M3 - Article

AN - SCOPUS:85064543670

SN - 0375-9601

VL - 383

SP - 2039

EP - 2045

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 17

ER -