On the characterization of vector rogue waves in two-dimensional two coupled nonlinear Schrödinger equations with distributed coefficients

Manikandan, K.; Senthilvelan, M.; Kraenkel, Roberto André

doi:10.1140/epjb/e2016-70420-0

Cited by 30 publications

(18 citation statements)

References 70 publications

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“…Besides temporal waveguides, such Manakov systems are relevant in other settings in optical physics too. For spatial solitons, diffraction will play the role of group velocity dispersion, and continuous variations of diffraction, nonlinearity, and gain/loss might lead to novel rogue wave patterns [47]. Similarly, Manakov soliton can arise for biased guest-host photorefractive polymer too [48].…”

Section: Discussionmentioning

confidence: 99%

Rogue Wave Modes for the Coupled Nonlinear Schrödinger System with Three Components: A Computational Study

Chan¹,

Chow²

2017

Applied Sciences

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Abstract:The system of "integrable" coupled nonlinear Schrödinger equations (Manakov system) with three components in the defocusing regime is considered. Rogue wave solutions exist for a restricted range of group velocity mismatch, and the existence condition correlates precisely with the onset of baseband modulation instability. This assertion is further elucidated numerically by evidence based on the generation of rogue waves by a single mode disturbance with a small frequency. This same computational approach can be adopted to study coupled nonlinear Schrödinger equations for the "non-integrable" regime, where the coefficients of self-phase modulation and cross-phase modulation are different from each other. Starting with a wavy disturbance of a finite frequency corresponding to the large modulation instability growth rate, a breather can be generated. The breather can be symmetric or asymmetric depending on the magnitude of the growth rate. Under the presence of a third mode, rogue wave can exist under a larger group velocity mismatch between the components as compared to the two-component system. Furthermore, the nonlinear coupling can enhance the maximum amplitude of the rogue wave modes and bright four-petal configuration can be observed.

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Section: Discussionmentioning

confidence: 99%

Rogue Wave Modes for the Coupled Nonlinear Schrödinger System with Three Components: A Computational Study

Chan¹,

Chow²

2017

Applied Sciences

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“…In a similar way, the CLMT can be employed to elucidate the underlying wave propagation phenomena of any physical system with propagating equations of the form of the coupled nonlinear Schrödinger equations, that is, our coupled local-mode equations when higher-order coupling, dispersive and nonlinear effects are omitted. Hence, exotic physical phenomena such as superposed nonlinear waves in coherently coupled Bose-Einstein condensates 57 , interacting rogue waves 58–60 or nonlinear ion-acoustic waves 61,62 can be explored in MCF media expanding the possibilities of single-core fibers. In the same line, additional physical phenomena such as relativistic effects could also be analysed using MCF media.…”

Section: Discussionmentioning

confidence: 99%

Ultra-short pulse propagation model for multi-core fibers based on local modes

Macho

García-Meca

Fraile-Peláez

et al. 2017

Sci Rep

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Multi-core fibers (MCFs) have sparked a new paradigm in optical communications and open new possibilities and applications in experimental physics and other fields of science, such as biological and medical imaging. In many of these cases, ultra-short pulse propagation is revealed as a key factor that enables us to exploit the full potential of this technology. Unfortunately, the propagation of such pulses in real MCFs has not yet been modelled considering polarization effects or typical random medium perturbations, which usually give rise to both longitudinal and temporal birefringent effects. Using the concept of local modes, we develop here an accurate ultra-short pulse propagation model that rigorously accounts for these phenomena in single-mode MCFs. Based on this theory, we demonstrate analytically and numerically the intermodal dispersion between different LP01 polarized core modes induced by these random perturbations when propagating femtosecond pulses in the linear and nonlinear fiber regimes. The ever-decreasing core-to-core distance significantly enhances the intermodal dispersion induced by these birefringent effects, which can become the major physical impairment in the single-mode regime. To demonstrate the power of our model, we give explicit strategies to reduce the impact of this optical impairment by increasing the MCF perturbations.

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“…The Peregrine solitons found profound interest in diverse areas of physics, namely, optical systems [278], BEC [73], hydrodynamics [12], and superfluids [25]. Originally, such Peregrine soliton solutions have been reported in the two-dimensional gradedindex waveguides using the similarity transformation [279], followed by their appearance in a two-dimensional graded-index grating waveguide [280] and two-dimensional coupled NLSEs with distributed coefficients [281]. The Peregrine soliton solutions in a (3 + 1)-D inhomogeneous NLSE with variable coefficients [282] and a (3 + 1)-D higher-order coupled NLSE [283] have also been reported.…”

Section: Peregrine Solitons In Higher Dimensional and Mixed Nlsesmentioning

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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On the characterization of vector rogue waves in two-dimensional two coupled nonlinear Schrödinger equations with distributed coefficients

Cited by 30 publications

References 70 publications

Rogue Wave Modes for the Coupled Nonlinear Schrödinger System with Three Components: A Computational Study

Rogue Wave Modes for the Coupled Nonlinear Schrödinger System with Three Components: A Computational Study

Ultra-short pulse propagation model for multi-core fibers based on local modes

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

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