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

Rahmi Rusin, Rudy Kusdiantara, Hadi Susanto

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)2039-2045
Number of pages7
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Issue number17
Publication statusPublished - 1 Jan 2019


  • Collisions
  • Dynamics of moving solitons
  • Integrable nonlocal nonlinear Schrödinger equation
  • Variational methods


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