On the characterization of breather and rogue wave solutions and modulation instability of a coupled generalized nonlinear Schrödinger equations

Priya, N. Vishnu; Senthilvelan, M.

doi:10.1016/j.wavemoti.2014.12.001

Cited by 29 publications

(8 citation statements)

References 25 publications

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“…The vector NLS equations yield potentially rich and significant results for optical fiber communication systems [12]. Motivated by this, several studies have also been undertaken to identify the localized solutions in coupled NLS equations with constant coefficients [33,34,35,36,37,38,39,40,41,42,43]. Subsequently attempts have been made to identify the localized solutions such as bright-bright, bright-dark, dark-dark soliton and RW solutions in the coupled vcNLS equations (in one-dimensions) [44,45,46,47,48,49,50,51].…”

Section: Introductionmentioning

confidence: 99%

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

2016

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Abstract. We construct vector rogue wave solutions of the two-dimensional two coupled nonlinear Schrödinger equations with distributed coefficients, namely diffraction, nonlinearity and gain parameters through similarity transformation technique. We transform the two-dimensional two coupled variable coefficients nonlinear Schrödinger equations into Manakov equation with a constraint that connects diffraction and gain parameters with nonlinearity parameter. We investigate the characteristics of the constructed vector rogue wave solutions with four different forms of diffraction parameters. We report some interesting patterns that occur in the rogue wave structures. Further, we construct vector dark rogue wave solutions of the two-dimensional two coupled nonlinear Schrödinger equations with distributed coefficients and report some novel characteristics that we observe in the vector dark rogue wave solutions.

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Section: Introductionmentioning

confidence: 99%

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

2016

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“…Modulation instability (MI) was a phenomenon firstly detected in hydrodynamic systems whereby water wave trains were found to disintegrate into irregular structures [6], being nowadays possibly associated with the underlying physical mechanisms responsible for the generation of soliton as well as rogue waves [2,13,17,22,32,33,35,42]. Moreover, its manifestation is now known to be commonly found in a myriad of nonlinear physical systems as a result of intensity-dependent perturbations due to the strong nonlinear effects that take place in nature.…”

Section: Introductionmentioning

confidence: 99%

Modulation instability in noninstantaneous Kerr media with walk-off and cross-phase modulation for mixed group-velocity-dispersion regimes

et al. 2016

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The dynamics of the modulation instability induced by cross phase modulation is studied by considering the influence of the walk-off and noninstantaneous response effects for two copropagating optical fields travelling in the anomalous regime of dispersion. To do so, we make use of extensions of the nonlinear Schrdinger equation jointly with the Debye model for polarization, which is shown to be effective and simplified when compared to the implementation of other methods for the noninstantaneous nonlinear response. In analyzing the sideband formation, two bands are observed with different behaviors with respect to the way the maximum gain and the respective frequency vary with increasing phase mismatch. Further, we also show that the manner in which the maximum gain as well as its corresponding frequency scale with the delay parameter τ is substantially different from the cases of both fields experiencing the normal group-velocity dispersion regime and the case of mixed regimes. These facts may give rise to many new possibilities for the evolution of the modulated wave when compared to the nonanomalous cases studied in the literature.

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“…Term Which Describes the Pulse Propagation in a Birefringent Fiber [193][194][195][196] iψ 1t + ψ 1xx + 2 a|ψ…”

Section: A Cnlse With the Four-wave Mixingmentioning

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 breather and rogue wave solutions and modulation instability of a coupled generalized nonlinear Schrödinger equations

Cited by 29 publications

References 25 publications

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

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

Modulation instability in noninstantaneous Kerr media with walk-off and cross-phase modulation for mixed group-velocity-dispersion regimes

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

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