Solitons in PT-symmetric periodic systems with the logarithmically saturable nonlinearity

Abstract

We report on the formation and stability of induced solitons in parity-time (PT) symmetric periodic systems with the logarithmically saturable nonlinearity. Both on-site and off-site lattice solitons exist for the self-focusing nonlinearity. The most intriguing result is that the above solitons can also be realized inside the several higher-order bands of the band structure, due to the change of nonlinear type with the soliton power. Stability analysis shows that on-site solitons are linearly stably, and off-site solitons are unstable in their existence domain.

A systematic construction of parity-time ($\mathcal{PT}$ )-symmetric and non-$\mathcal{PT}$ -symmetric complex potentials from the solutions of various real nonlinear evolution equations

“…These elliptic functions sn, cn and dn are doubly periodic functions having periods 4K, 4K and 2K respectively. One can easily obtain the following solution from solution (20) by considering the initial time t 0 such that δ 5 (t 0 ) = bt 0 + s 0 = 0 and δ 6 (t 0 ) = dt 0 + r 0 = 0…”

“…In particular, the existence of different nonlinear localized modes has been studied analytically as well as numerically in the nonlinear Schrödinger (NLS) equation with complex PT symmetric periodic potential [5], Scarf-II potential [12], Gaussian potential [13], Bessel potential [14], Rosen-Morse potential [15], and harmonic potential [16]. In addition to these, nonlinear modes have been studied for other complex PT -symmetric potentials bearing nonlinear optical systems such as competing nonlinearity [17], saturable nonlinearity [18], and logarithmically saturable nonlinearity [19]. On the other hand the complex potentials are also used in BEC to explore nonlinear localized modes [20].…”

New features of the surface wave propagation along an exponentially graded-index layer and nonlinear substrate with generalized Kerr-type nonlinear response

“…Many different forms of non-Kerr nonlinearity are known to date, for which nonlinear waves are described by exact analytical solutions to the wave equation [9]. These include photorefractive [10], logarithmic [11], power [12], saturable [13], and its various generalizations [14,15], stepwise [16,17] nonlinearities. The authors of [18,19] note that stepwise nonlinearities can be applied to the media characterized by optical bistability.…”

Особенности Формирования Локализованных Состояний Вблизи Плоского Дефекта В Средах Со Скачкообразно Меняющимся Дефокусирующим Нелинейным Откликом

“…Для теоретического описания ряда свойств такого вида нелинейно-оптических сред часто применяется нелинейное уравнение Шредингера (НУШ) [4]. Помимо классической формы НУШ с кубической нелинейностью для описания иных видов нелинейного отклика среды используются обобщения НУШ, содержащие степенную, полиномиальную, логарифмическую, насыщаемую и ступенчатую нелинейности [5][6][7][8][9][10][11]. Следует отметить универсальность таких моделей, находящих применение для теоретического описания бозе-эйнштейновской конденсации (БЭК) для атомов под названием уравнения Гросса−Питаевского [12], а для экситонного или поляритонного конденсатов в полупроводниках -уравнения Келдыша [13].…”