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 -