Solitonic dynamics and excitations of the nonlinear Schrödinger equation with third-order dispersion in non-Hermitian PT-symmetric potentials

Chen, Yong; Yan, Zhenya

doi:10.1038/srep23478

Cited by 47 publications

(10 citation statements)

References 61 publications

(134 reference statements)

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“…We will discuss on this subject in a separated literature. The similar discussions can be made to obtain more complicated quantum wells, even for NLS with Parity-Time symmetry potential cases [36,37]. and − f 2 respectively.…”

Section: Eigen-state In a Complicated Quantum Well Generated Frommentioning

confidence: 73%

Solitons in nonlinear systems and eigen-states in quantum wells

Zhao

Yang

2019

Chinese Phys. B

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We study the relations between solitons of nonlinear Schrödinger equation described systems and eigen-states of linear Schrödinger equation with some quantum wells. Many different nondegenerated solitons are re-derived from the eigen-states in the quantum wells. We show that the vector solitons for coupled system with attractive interactions correspond to the identical eigenstates with the ones of coupled systems with repulsive interactions. The energy eigenvalues of them seem to be different, but they can be reduced to identical ones in the same quantum wells. The non-degenerated solitons for multi-component systems can be used to construct much abundant degenerated solitons in more components coupled cases. On the other hand, we demonstrate soliton solutions in nonlinear systems can be also used to solve the eigen-problems of quantum wells. As an example, we present eigenvalue and eigen-state in a complicated quantum well for which the Hamiltonian belongs to the non-Hermitian Hamiltonian having Parity-Time symmetry. We further present the ground state and the first exited state in an asymmetric quantum double-well from asymmetric solitons. Based on these results, we expect that many nonlinear physical systems can be used to observe the quantum states evolution of quantum wells, such as water wave tank, nonlinear fiber, Bose-Einstein condensate, and even plasma, although some of them are classical physical systems. These relations provide another different way to understand the stability of solitons in nonlinear Schrödinger equation described systems, in contrast to the balance between dispersion and nonlinearity.

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Section: Eigen-state In a Complicated Quantum Well Generated Frommentioning

confidence: 73%

Solitons in nonlinear systems and eigen-states in quantum wells

Zhao

Yang

2019

Chinese Phys. B

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“…which are a standard reflectionless potential [70,71] and a gain-loss distribution for the excitations respectively [21][22][23][24]. Together, they form a modified (hyperbolic) Scarf-II potential with the following properties [21]:…”

Section: Bogoliubov-de Gennes Equationsmentioning

confidence: 99%

Stability of matter-wave solitons in a density-dependent gauge theory

Dingwall

Öhberg

2019

Phys. Rev. A

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We consider the linear stability of chiral matter-wave solitons described by a density-dependent gauge theory. By studying the associated Bogoliubov-de Gennes equations both numerically and analytically, we find that the stability problem effectively reduces to that of the standard Gross-Pitaevskii equation, proving that the solitons are stable to linear perturbations. In addition, we formulate the stability problem in the framework of the Vakhitov-Kolokolov criterion and provide supplementary numerical simulations which illustrate the absence of instabilities when the soliton is initially perturbed.

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“…Here, we elaborate three different scenario of dynamical control of nonlinear localized modes, making use of adiabatically varying parameters of the potential 38 , 53 – 55 , m 0 → m 0 ( z ) or θ 0 → θ 0 ( z ). We choose the following temporal-modulation pattern: …”

Section: Resultsmentioning

confidence: 99%

“…In particular, optical solitons can utilize the nonlinearity in optical fibers to balance the group-velocity dispersion, thus stably propagating in long-scale telecommunication links. More recently, stable -symmetric solitons were also investigated in the third-order NLS equation 53 , the generalized GP equation with a variable group-velocity coefficient 54 , and the derivative NLS equation 55 . The vast work performed in the field of nonlinear waves in -symmetric systems has been summarized in two recent comprehensive reviews 56 , 57 .…”

Section: Introductionmentioning

confidence: 99%

Families of stable solitons and excitations in the PT-symmetric nonlinear Schrödinger equations with position-dependent effective masses

Chen

Yan

Mihalache

et al. 2017

Sci Rep

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Since the parity-time-(-) symmetric quantum mechanics was put forward, fundamental properties of some linear and nonlinear models with -symmetric potentials have been investigated. However, previous studies of -symmetric waves were limited to constant diffraction coefficients in the ambient medium. Here we address effects of variable diffraction coefficient on the beam dynamics in nonlinear media with generalized -symmetric Scarf-II potentials. The broken linear symmetry phase may enjoy a restoration with the growing diffraction parameter. Continuous families of one- and two-dimensional solitons are found to be stable. Particularly, some stable solitons are analytically found. The existence range and propagation dynamics of the solitons are identified. Transformation of the solitons by means of adiabatically varying parameters, and collisions between solitons are studied too. We also explore the evolution of constant-intensity waves in a model combining the variable diffraction coefficient and complex potentials with globally balanced gain and loss, which are more general than -symmetric ones, but feature similar properties. Our results may suggest new experiments for -symmetric nonlinear waves in nonlinear nonuniform optical media.

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Solitonic dynamics and excitations of the nonlinear Schrödinger equation with third-order dispersion in non-Hermitian PT-symmetric potentials

Cited by 47 publications

References 61 publications

Solitons in nonlinear systems and eigen-states in quantum wells

Solitons in nonlinear systems and eigen-states in quantum wells

Stability of matter-wave solitons in a density-dependent gauge theory

Families of stable solitons and excitations in the PT-symmetric nonlinear Schrödinger equations with position-dependent effective masses

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