Binding energy of soliton molecules in time-dependent harmonic potential and nonlinear interaction

Khawaja, U. Al; Boudjemâa, Abdelâali

doi:10.1103/physreve.86.036606

Cited by 11 publications

(4 citation statements)

References 18 publications

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“…Various analytical methods are used to solve different versions of the NLSE such as the inverse scattering transform [86][87][88][89][90][91][92][93], the Adomian Decomposition method [94], the Homotopy Analysis method [95,96], the similarity transformation method [97][98][99][100][101][102], and the Darboux transformation and Lax pair method [103][104][105][106], just to name a few. This section is devoted to deriving the general breather solution of the fundamental NLSE using the Darboux transformation and Lax pair method [107].…”

Section: Analytical Derivation Of the Fundamental Peregrine Solitonmentioning

confidence: 99%

Peregrine Solitons of the Higher-Order, Inhomogeneous, Coupled, Discrete, and Nonlocal Nonlinear Schrödinger Equations

2020

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This study reviews the Peregrine solitons appearing under the framework of a class of nonlinear Schrödinger equations describing the diverse nonlinear systems. The historical perspectives include the various analytical techniques developed for constructing the Peregrine soliton solutions, followed by the derivation of the general breather solution of the fundamental nonlinear Schrödinger equation through Darboux transformation. Subsequently, we collect all forms of nonlinear Schrödinger equations, involving systematically the effects of higher-order nonlinearity, inhomogeneity, external potentials, coupling, discontinuity, nonlocality, higher dimensionality, and nonlinear saturation in which Peregrine soliton solutions have been reported.

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Section: Analytical Derivation Of the Fundamental Peregrine Solitonmentioning

confidence: 99%

Peregrine Solitons of the Higher-Order, Inhomogeneous, Coupled, Discrete, and Nonlocal Nonlinear Schrödinger Equations

2020

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“…Soliton molecules (SM) attract significant fundamental and practical interest [1][2][3][4][5]. Previous decades of research revealed a plethora of soliton molecule types including: SM with independently evolving phase and flipping phase, group-velocitylocked vector SM [6], etc.…”

Section: Introductionmentioning

confidence: 99%

All-polarisation-maintaining modified figure-of-8 fibre laser as a source of soliton molecules

et al. 2020

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The conditions are identified, under which a figure-of-eight all-polarisation-maintaining fibre laser with two independently pumped active media, each in one of the two cavity loops, generates soliton molecules with adjustable number of solitons in the molecule. The soliton count in the molecule may be reproducibly set between 2 and 6 by adjustment of the ratio of the pump powers of the active media. The average duration of the autocorrelation function of a single soliton is 11.6 ps, the repetition rate of the pulse train is 14.19 MHz, and its average spectral width is 10 nm. An analysis of the map of the mode-locked regimes set by different ratios of the pump source powers has shown that there exist two separate areas, one corresponding to generation of noise-like pulses and the other, to generation of soliton molecules. We believe that our findings will extend the application area of soliton molecules and will further bring a new insight into understanding of soliton molecule formation inside fibre cavities.

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“…Through the GP equation with constant and oscillatory part of the contact interaction, Saito and Ueda stabilized the trapless matter-wave bright solitons in 2D by temporal modulation of contact interaction [48], Adhikari examined the problem and stabilized the untrapped soliton in 3D and the vortex soliton in 2D by temporal modulation of contact interaction [46]. Effects of the time-dependent nonlinear contact interaction on the binding energy of soliton molecules has been examined by Khawaja and Boudjemaa [47]. We have studied the stability of the 3D BEC with constant and oscillatory part for both the two-and three-body interactions in our previous work [45].…”

Section: Introductionmentioning

confidence: 99%

Stabilization of trapless dipolar Bose-Einstein condensates by temporal modulation of the contact interaction

Sabari

Dey

2018

Phys. Rev. E

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We theoretically study the stability of a trapless dipolar Bose-Einstein condensate (BEC) with temporal modulation of short-range contact interaction. For this aim, through both analytical and numerical methods, we solve a Gross-Pitaevskii equation with both constant and oscillatory form of short-range contact interaction along with long-range, nonlocal, dipole-dipole (DD) interaction terms. Using variational method, we discuss the stability of the trapless dipolar BEC with presence and absence of both constant and oscillatory contact interactions. We show that the oscillatory contact interaction prevents the collapse of the trapless dipolar BEC. We confirm the analytical prediction through numerical simulations. We have also studied the collective excitations in the system induced by the effective potential due to oscillating interaction. PACS numbers: 03.75.-b, 05.45.-a, 05.45.Yv, 03.75.Lm

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Binding energy of soliton molecules in time-dependent harmonic potential and nonlinear interaction

Cited by 11 publications

References 18 publications

Peregrine Solitons of the Higher-Order, Inhomogeneous, Coupled, Discrete, and Nonlocal Nonlinear Schrödinger Equations

Peregrine Solitons of the Higher-Order, Inhomogeneous, Coupled, Discrete, and Nonlocal Nonlinear Schrödinger Equations

All-polarisation-maintaining modified figure-of-8 fibre laser as a source of soliton molecules

Stabilization of trapless dipolar Bose-Einstein condensates by temporal modulation of the contact interaction

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