Dark and antidark soliton interactions in the nonlocal nonlinear Schrödinger equation with the self-induced parity-time-symmetric potential

Abstract

Via the Nth Darboux transformation, a chain of nonsingular localized-wave solutions is derived for a nonlocal nonlinear Schrödinger equation with the self-induced parity-time (PT) -symmetric potential. It is found that the Nth iterated solution in general exhibits a variety of elastic interactions among 2N solitons on a continuous-wave background and each interacting soliton could be the dark or antidark type. The interactions with an arbitrary odd number of solitons can also be obtained under different degenerate conditions. With N=1 and 2, the two-soliton and four-soliton interactions and their various degenerate cases are discussed in the asymptotic analysis. Numerical simulations are performed to support the analytical results, and the stability analysis indicates that the PT-symmetry breaking can also destroy the stability of the soliton interactions.

Darboux Transformations and Global Explicit Solutions for Nonlocal Davey–Stewartson I Equation

“…In [1], Ablowitz and Musslimani introduced the nonlocal nonlinear Schrödinger equation and got its explicit solutions by inverse scattering. Quite a lot of work was done after that for this equation and the others [2][3][4][5][6][7][8][9][10][11][12][13][14].…”

Peregrine rogue wave dynamics in the continuous nonlinear Schrödinger system with parity-time symmetric Kerr nonlinearity

“…It is worthwhile to mention that the idea of parity-time symmetry and the transverse shift, in the context of Rogue waves, have also been explored by a group of researchers [33,34]. Other works in this connection include dark and antidark soliton interactions in the nonlocal nonlinear Schrödinger equation with self-induced parity-time-symmetric potential [35], periodic and hyperbolic soliton solutions in nonlocal PTsymmetric equations [36]. On a different side, as a limiting case of a wide class of solutions to the nonlinear Schrödinger equations, Peregrine solitons (PSs) being localized both in evolution and transverse variables draws fundamental importance [37].…”

Generalized Darboux Transformation and Rational Solutions for the Nonlocal Nonlinear Schrödinger Equation with the Self-Induced Parity-Time Symmetric Potential

“…The dark and antidark soliton interactions have been given in [18] via the classical Darboux transformation (DT) method. However, there are no papers on high-order rational solutions of Equation (1) by generalized Darboux transformation (gDT).…”

“…The compatibility condition 0 z x U V UV VU − + − = is equivalent to Equation (1) by a direct computation. The classical DT for Equation (1) has been constructed in [18]:…”