Rotation of the trajectories of bright solitons and realignment of intensity distribution in the coupled nonlinear Schrödinger equation

Radha, R.; Vinayagam, P. S.; Porsezian, K.

doi:10.1103/physreve.88.032903

Cited by 15 publications

(9 citation statements)

References 26 publications

(23 reference statements)

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“…is the transformed field and σ = Φ 0 Λ Φ −1 0 and Φ 0 is a known solution of the linear system (5), we apply the DT on the linear system given by Eqs. (4), and the stipulation that the transformed linear system be covariant with the original one requires…”

Section: Darboux Transformation With Zero Seed: Single Soliton Solutionmentioning

confidence: 99%

“…UAK and PSV acknowledge the support of UAE University through the grant UAEU-UPAR (7) and UAEU-UPAR (4). RR wishes to acknowledge the financial assistance received from Department of Atomic Energy-National…”

Section: Acknowledgementsmentioning

confidence: 99%

“…Eq. (1) has been shown to be integrable if either (i) g 11 = g 12 =g 21 =g 22 or (ii) g 11 = g 21 =-g 12 =-g 22 [4]. The first choice corresponds to Manakov model [5] while the second choice represents the modified Manakov model [6].…”

Section: Introductionmentioning

confidence: 99%

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New classes of solutions in the coupled PT symmetric nonlocal nonlinear Schrödinger equations with four wave mixing

Vinayagam

Radha²,

Khawaja

et al. 2018

Communications in Nonlinear Science and Numerical Simulation

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We investigate generalized nonlocal coupled nonlinear Schorödinger equation containing Self-Phase Modulation, Cross-Phase Modulation and Four Wave Mixing involving nonlocal interaction. By means of Darboux transformation we obtained a family of exact breathers and solitons including the Peregrine soliton, Kuznetsov-Ma breather, Akhmediev breather along with all kinds of soliton-soliton and breather-soltion interactions. We analyze and emphasize the impact of the four-wave mixing on the nature and interaction of the solutions. We found that the presence of Four Wave Mixing converts a two-soliton solution into an Akhmediev breather. In particular, the inclusion of Four Wave Mixing results in the generation of a new solutions which is spatially and temporally periodic called "Soliton (Breather) lattice".

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Section: Darboux Transformation With Zero Seed: Single Soliton Solutionmentioning

confidence: 99%

Section: Acknowledgementsmentioning

confidence: 99%

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New classes of solutions in the coupled PT symmetric nonlocal nonlinear Schrödinger equations with four wave mixing

Vinayagam

Radha²,

Khawaja

et al. 2018

Communications in Nonlinear Science and Numerical Simulation

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“…For condensates in a time independent harmonic trap, λ(t) = λ 0 (a constant), Equation (11) yields γ(t) = γ 0 exp (λ 0 t), where γ 0 is an arbitrary constant. Considering a vacuum seed solution, i.e., q 1 (x, t) = q 2 (x, t) = 0, and employing gauge transformation approach [39][40][41][42], we obtain…”

Section: The Model and Lax Pairmentioning

confidence: 99%

Bright soliton dynamics in spin orbit-Rabi coupled Bose-Einstein condensates

Vinayagam

Radha²,

Bhuvaneswari

et al. 2017

Communications in Nonlinear Science and Numerical Simulation

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We investigate the dynamics of a spin-orbit (SO) coupled BECs in a time dependent harmonic trap and show the dynamical system to be completely integrable by constructing the Lax pair. We then employ gauge transformation approach to witness the rapid oscillations of the condensates for a relatively smaller value of SO coupling in a time independent harmonic trap compared to their counterparts in a transient trap. Keeping track of the evolution of the condensates in a transient trap during its transition from confining to expulsive trap, we notice that they collapse in the expulsive trap. We further show that one can manipulate the scattering length through Feshbach resonance to stretch the lifetime of the confining trap and revive the condensate. Considering a SO coupled state as the initial state, the numerical simulation indicates that the reinforcement of Rabi coupling on SO coupled BECs generates the striped phase of the bright solitons and does not impact the stability of the condensates despite destroying the integrability of the dynamical system.

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“…where q i (x, t)(i=1,2) corresponds to the envelope of the electromagnetic radiation passing through the optical fibre and i is the imaginary unit. In the above equation, g 11 and g 22 correspond to the Self Phase Modulation (SPM) while g 12 and g 21 represent the Cross Phase Modulation (XPM). Equations.…”

Section: Introductionmentioning

confidence: 99%

Manipulation of light in a generalized coupled Nonlinear Schrödinger equation

Radha¹,

Vinayagam²,

Porsezian

2016

Communications in Nonlinear Science and Numerical Simulation

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We investigate a generalized coupled nonlinear Schrodinger (GCNLS) equation containing Self-Phase Modulation (SPM), Cross-Phase Modulation (XPM) and Four Wave Mixing (FWM) describing the propagation of electromagnetic radiation through an optical fibre and generate the associated Lax-pair. We then construct bright solitons employing gauge transformation approach. The collisional dynamics of bright solitons indicates that it is not only possible to manipulate intensity (energy) between the two modes (optical beams), but also within a given mode unlike the Manakov model which does not have the same freedom. The freedom to manipulate intensity (energy) in a given mode or between two modes arises due to a suitable combination of SPM, XPM and FWM. While SPM and XPM are controlled by an arbitrary real parameter each, FWM is governed by two arbitrary complex parameters. The above model may have wider ramifications in nonlinear optics and Bose-Einstein Condensates (BECs).

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Rotation of the trajectories of bright solitons and realignment of intensity distribution in the coupled nonlinear Schrödinger equation

Cited by 15 publications

References 26 publications

New classes of solutions in the coupled PT symmetric nonlocal nonlinear Schrödinger equations with four wave mixing

New classes of solutions in the coupled PT symmetric nonlocal nonlinear Schrödinger equations with four wave mixing

Bright soliton dynamics in spin orbit-Rabi coupled Bose-Einstein condensates

Manipulation of light in a generalized coupled Nonlinear Schrödinger equation

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