TY - JOUR

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

AU - Rusin, Rahmi

AU - Kusdiantara, Rudy

AU - Susanto, Hadi

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

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

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

SN - 0375-9601

ER -