Analytical stable Gaussian soliton supported by a parity-time symmetric potential with power-law nonlinearity

Abstract

We address the existence and stability of spatial localized modes supported by a parity-time-symmetric complex potential in the presence of power-law nonlinearity. The analytical expressions of the localized modes, which are Gaussian in nature, are obtained in both (1+1) and (2+1) dimensions. A linear stability analysis corroborated by the direct numerical simulations reveals that these analytical localized modes can propagate stably for a wide range of the potential parameters and for various order nonlinearities. Some dynamical characteristics of these solutions, such as the power and the transverse power-flow density, are also examined.

Solitons in a nonlinear Schrödinger equation withPT-symmetric potentials and inhomogeneous nonlinearity: Stability and excitation of nonlinear modes

“…(17)] while the real part of the potential U ǫ (x) preserves a double-well shape. Nonlinear modes in this case were recently reported in [17,30] (also, nonlinear modes in a slightly different double well potential with the imaginary part (33b) was investigated in [29]). When α increases of the amplitude of the potential barrier between the humps decreases.…”

Exactly Solvable Wadati Potentials in the PT-Symmetric Gross-Pitaevskii Equation

“…Once µ(z) has been chosen, the first equation in (10) gives a(z) while equation (11) together with the second equation in (10) produce θ (z). The corresponding potential base function A(z) is given by (12).…”

“…Stimulated by the interest from the atomic physics and optics, a number of exactly-solvable Gross-Pitaevskii equations was identified, both within and outside the PT-symmetric variety. The list includes periodic complex potentials [8,9]; the PT-symmetric Scarff II [6,10] and Rosen-Morse II potentials [11], as well as a PT-symmetric double-well superposition of a quadratic and a gaussian [12].…”

Connected and disconnected stable regions of solitons of nonlinear Schrödinger equation with $\mathcal{PT}$-symmetric potential

“…In the last decades, the theory of existence of nonlinear localized modes in PT symmetric potential and their linear stability has been studied very promptly [22,23]. Several interesting potentials for example Scarf-II potential [24], harmonic potential [25], Rosen-Morse potential [26], Gaussian potential [27][28][29][30][31][32], sextic anharmonic double-well potential [33], time-dependent harmonic-Gaussian potential [34] etc are considered for study.…”