Nonautonomous soliton, controllable interaction and numerical simulation for generalized coupled cubic–quintic nonlinear Schrödinger equations

Yu, Fajun

doi:10.1007/s11071-016-2754-9

Cited by 16 publications

(5 citation statements)

References 39 publications

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“…Thus, nonautonomous nonlinear Schrödinger equations have received huge impact in recent years due to their attractiveness and their peculiar properties for some potential applications. With the advancement of modern nonlinear theory, the management and control of nonautonomous solitons is hot topic in the modern optical communication [19]. Recently, solitons with nonautonomous terms are reported for resonant nonlinear Schrödinger (vc-RNLS) equation with inhomogeneous functions [20].…”

Section: Introductionmentioning

confidence: 99%

Transition from bird to butterfly shaped nonautonomous soliton and soliton switching in erbium doped resonant fiber

Rajan¹

2020

Phys. Scr.

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Through theoretical approach, two soliton solutions for nonautonomous inhomogeneous nonlinear Schrödinger - Maxwell Bloch (INLS-MB) equation is attained with the aid of Darboux transformation technique. Based on obtained solutions, bird and butterfly like wave pattern are attained for the specific choice of inhomogeneous coefficients. Especially, by means of dispersion management scheme, exponential profile is adopted for the dispersion coefficient in the governing two soliton solutions. Also, through the appropriate choices of control parameters in inhomogeneous function, the transition from bird shaped to butterfly shaped pulse is observed astoundingly. Finally, nonautonomous soliton switching achieved through soliton fission and fusion phenomenon which could be observed via properly manipulating dispersion and nonlinearity parameters. The obtained analytical results and graphical illustrations are may helpful for the design of soliton control system in fiber optic communication and soliton based optical switching.

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Section: Introductionmentioning

confidence: 99%

Transition from bird to butterfly shaped nonautonomous soliton and soliton switching in erbium doped resonant fiber

Rajan¹

2020

Phys. Scr.

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“…In this way, vector solitons have been identified upon considering e.g. temporal [71][72][73] and spatial [74][75][76] variations of the scattering lengths. In the same context control over the system's parameters has been examined by performing temporal modulations of the confinement frequencies [71][72][73] and also by adding appropriate time-dependent gain and loss terms [24,60].…”

Section: Introductionmentioning

confidence: 99%

“…temporal [71][72][73] and spatial [74][75][76] variations of the scattering lengths. In the same context control over the system's parameters has been examined by performing temporal modulations of the confinement frequencies [71][72][73] and also by adding appropriate time-dependent gain and loss terms [24,60]. Moreover, control over the system's dynamical evolution and pattern formation has been reported in [77], upon quenching the binary BEC towards miscibility.…”

Section: Introductionmentioning

confidence: 99%

Spontaneous generation of dark-bright and dark-antidark solitons upon quenching a particle-imbalanced bosonic mixture

Kiehn¹,

Mistakidis²,

Katsimiga³

et al. 2019

Phys. Rev. A

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We unveil the dynamical formation of multiple localized structures in the form of dark-bright and dark-antidark solitary waves that emerge upon quenching a one-dimensional particle-imbalanced Bose-Bose mixture. Interspecies interaction quenches drive the system out-of-equilibrium while the so-called miscible/immiscible threshold is crossed in a two directional manner. Dark-bright entities are spontaneously generated for quenches towards the phase separated regime and dark-antidark states are formed in the reverse process. The distinct mechanisms of creation of the aforementioned states are discussed in detail and their controlled generation is showcased. In both processes, it is found that the number of solitary waves generated is larger for larger particle imbalances, a result that is enhanced for stronger postquench interspecies interactions. Additionally the confining geometry highly affects the production of both types of states with a decaying solitary wave formation occurring for tighter traps. Furthermore, in both of the aforementioned transitions, the breathing frequencies measured for the species differ significantly for highly imbalanced mixtures. Finally, the robustness of the dynamical formation of dark-bright and dark-antidark solitons is also demonstrated in quasi one-dimensional setups.arXiv:1902.09316v3 [cond-mat.quant-gas]

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“…The form of soliton is mainly obtained by decoupling the equation. For the interaction process of solitons, it can be observed, verified and tested by numerical simulation [5][6]. There are many methods of numerical simulation, and the most commonly used method is the finite difference method.…”

Section: Introductionmentioning

confidence: 99%

Motion and Interaction of Envelope Solitons in Schrödinger Equation Simulated by Symplectic Algorithm

Lianyou¹

2019

AJPA

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The expression of Gaussian envelope soliton in Schrödinger equations are given and proved in this paper. According to the characteristics of the Gauss envelope soliton, further proposed that the interaction between Gaussian envelope solitons exists in Schrödinger equation. The symplectic algorithm for solving Schrödinger equation is proposed after analysis characteristics of Schrödinger equation. First, the Schrödinger equation is transformed into the standard Hamiltonian canonical equation by separating the real and imaginary parts of wave function. Secondly, the symplectic algorithm is implemented by using the Euler center difference method for the canonical equation. The conserved quantity of symplectic algorithm is given, and the stability of symplectic algorithm is proved. The numerical simulation experiment was carried out on Schrödinger equation in Gauss envelope soliton motion and multi solitons interaction. The experimental results show that the proposed method is correct and the symplectic algorithm is effective.

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Nonautonomous soliton, controllable interaction and numerical simulation for generalized coupled cubic–quintic nonlinear Schrödinger equations

Cited by 16 publications

References 39 publications

Transition from bird to butterfly shaped nonautonomous soliton and soliton switching in erbium doped resonant fiber

Transition from bird to butterfly shaped nonautonomous soliton and soliton switching in erbium doped resonant fiber

Spontaneous generation of dark-bright and dark-antidark solitons upon quenching a particle-imbalanced bosonic mixture

Motion and Interaction of Envelope Solitons in Schrödinger Equation Simulated by Symplectic Algorithm

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