Variational approximations of soliton dynamics in the Ablowitz-Musslimani nonlinear Schrödinger equation
arXiv:1905.09112 · doi:10.1016/j.physleta.2019.03.043
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 () 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.
arXiv commentPhys. Lett. A (2019)
References in corpus (10)
- Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
- Making Sense of Non-Hermitian Hamiltonians
- PT-Symmetric Quantum Mechanics
- Nonlinear waves in -symmetric systems
- Nonlinear switching and solitons in PT-symmetric photonic systems
- General soliton solution to a nonlocal nonlinear Schrödinger equation with zero and nonzero boundary conditions
- Darboux transformations and global solutions for a nonlocal derivative nonlinear Schrodinger equation
- Periodic and Hyperbolic Soliton Solutions of a Number of Nonlocal PT-Symmetric Nonlinear Equations
- Variational approximation and the use of collective coordinates
- Variational approximations using Gaussian ansatz, false instability, and its remedy in nonlinear Schrödinger lattices