Rogue waves for the coupled variable-coefficient fourth-order nonlinear Schrödinger equations in an inhomogeneous optical fiber

Du, Zhong; Tian, Bo; Chai, Han-Peng; Sun, Yuekai; Zhao, Xue-Hui

doi:10.1016/j.chaos.2018.02.017

Cited by 86 publications

(27 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Nonlinear dynamics of the two-mode electric field with amplitudes q 1,2 and formation of rogue waves are described by the following system of coupled equations [54] t ¶ ¶ + ¶ ¶ + + = Î q x q q q q n i 1 2 0, 1, 2 . This coupled system can be extended to describe other physical systems by adding higher-order effects to coupled NLSEs [57]. However, we neglect effects due to these nonlinear dynamical evolution terms in the coupled nonlinear SPWs as these nonlinear terms are related to higher-order dispersion and nonlinearities, thereby leading to distinct rogue-wave and polarization-modulation instability properties.…”

Section: Modulation Instability and Dark Rogue Wavesmentioning

confidence: 99%

Surface-polaritonic phase singularities and multimode polaritonic frequency combs via dark rogue-wave excitation in hybrid plasmonic waveguide

et al. 2020

View full text Add to dashboard Cite

Material characteristics and input-field specifics limit controllability of nonlinear electromagneticfield interactions. As these nonlinear interactions could be exploited to create strongly localized bright and dark waves, such as nonlinear surface polaritons, ameliorating this limitation is important. We present our approach to amelioration, which is based on a surface-polaritonic waveguide reconfiguration that enables excitation, propagation and coherent control of coupled dark rogue waves having orthogonal polarizations. Our control mechanism is achieved by finely tuning laser-field intensities and their respective detuning at the interface between the atomic medium and the metamaterial layer. In particular, we utilize controllable electromagnetically induced transparency windows commensurate with surface-polaritonic polarization-modulation instability to create symmetric and asymmetric polaritonic frequency combs associated with dark localized waves. Our method takes advantage of an atomic self-defocusing nonlinearity and dark rogue-wave propagation to obtain a sufficient condition for generating phase singularities. Underpinning this method is our theory which incorporates dissipation and dispersion due to the atomic medium being coupled to nonlinear surface-polaritonic waves. Consequently, our waveguide configuration acts as a bimodal polaritonic frequency-comb generator and high-speed phase rotator, thereby opening prospects for phase singularities in nanophotonic and quantum communication devices.field [18]. In the past few decades, experimental and theoretical investigations(for an intuitive explanation of dealing with plasmonic loss for waveguide application, see [19]) report stable propagation of linear and nonlinear SPWs employing ultra-low loss metallic-type layers such as single-crystal [20] and mono-crystal [21] metallic film, structured Fano metamaterials [22], semiconductor metamaterials [23] and superconducting metamaterials [24]. These investigations reveal that plasmonic excitation and stable propagation need minimal metallic nanostructure roughness [25]. Therefore, polaritonic frequency combs, and generally space-time control of nonlinear SPWs, are unfortunately challenging due to material limitations and driving field characteristics [26-28].Propagation of an optical pulse in nonlinear media leads to the appearance of strongly localized bright and dark waves such as soliton [29], rogue waves and breathers in nearly conservative systems [30]. Bright rogue waves and breathers are highly localized nonlinear solitary waves with oscillatory amplitudes [31,32]. These waves are valuable for their applications to phase and intensity modulation schemes [33,34], as well as the formation of bound states and molecule-like behavior [35]. More generally, dissipative rogue waves and breathers [36] have potential applications to nonlinear systems such as mode-locked lasers [37] and frequencycomb generators [38]. By contrast, dark rogue waves were only observed during multimode polarized light propagation ...

show abstract

Section: Modulation Instability and Dark Rogue Wavesmentioning

confidence: 99%

Surface-polaritonic phase singularities and multimode polaritonic frequency combs via dark rogue-wave excitation in hybrid plasmonic waveguide

et al. 2020

View full text Add to dashboard Cite

show abstract

“…On the other hand, when the inhomogeneities of media are taken into account, that is the NLEE are considered with space variable coefficients. This case represents more realistic models than those which are considered with constant coefficients . The soliton wave propagation in the above‐mode has been called “non‐autonomous soliton.” Hence, N‐soliton nonautonomous soliton interactions in various play a definitive role in the formation of the structure of wave and also the propagation direction with a phase shift in dispersive media …”

Section: Introductionmentioning

confidence: 99%

On multiple soliton similariton‐pair solutions, conservation laws via multiplier and stability analysis for the Whitham–Broer–Kaup equations in weakly dispersive media

Abdel‐Gawad

Tantawy

Yusuf

2019

Math Methods in App Sciences

View full text Add to dashboard Cite

In this article, the generalized unified method (GUM) is used for finding multiwave solutions of the coupled Whitham‐Broer‐Kaup (WBK) equation with variable coefficients. Which describes the propagation of of shallow water waves. Here, we study the effects of the indirect nonlinear interaction of one‐, two‐ and three‐solitonic similaritons on the behavior of propagation of waves, in quasi‐periodic distributed system. This study can unable us to control the dynamics of type soliton (soliton, anti‐soliton) similaritons waves in dispersive waveguides. To give more physical insight to the obtained solutions, they are shown graphically. Their different structures are depicted by taking appropriate arbitrary functions. Further, with the suitable parameters, the indirect nonlinear interaction between two and three‐soliton waves are shown weal, in the sense that their amplitude does not blow up. Moreover, because of the importance of conservation laws Cls and stability analysis SA in the investigation of integrability, internal properties, existence, and uniqueness of a differential equation, we compute the Cls via multiplier technique and stability analysis via the concept of linear stability analysis for the WBK equations using the constant coefficients.

show abstract

“…In the applied science, NLEEs are extensively used in theoretical studies to model a wide range of nonlinear phenomena. To comprehend the mechanisms of nonlinear phenomena, it is vital to investigate the solutions of NLEEs [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. One specific tool that has recently achieved a special interest from academic researchers is the multiple exp-function scheme [16,17].…”

Section: Introductionmentioning

confidence: 99%

Multiple Soliton Solutions of the Sawada-Kotera Equation with a Nonvanishing Boundary Condition and the Perturbed Korteweg de Vries Equation by Using the Multiple Exp-Function Scheme

Adem

Mirzazadeh

Zhou

et al. 2019

Advances in Mathematical Physics

View full text Add to dashboard Cite

The Sawada-Kotera equation with a nonvanishing boundary condition, which models the evolution of steeper waves of shorter wavelength than those depicted by the Korteweg de Vries equation, is analyzed and also the perturbed Korteweg de Vries (pKdV) equation. For this goal, a capable method known as the multiple exp-function scheme (MEFS) is formally utilized to derive the multiple soliton solutions of the models. The MEFS as a generalization of Hirota's perturbation method actually suggests a systematic technique to handle nonlinear evolution equations (NLEEs).

show abstract

Rogue waves for the coupled variable-coefficient fourth-order nonlinear Schrödinger equations in an inhomogeneous optical fiber

Cited by 86 publications

References 34 publications

Surface-polaritonic phase singularities and multimode polaritonic frequency combs via dark rogue-wave excitation in hybrid plasmonic waveguide

Surface-polaritonic phase singularities and multimode polaritonic frequency combs via dark rogue-wave excitation in hybrid plasmonic waveguide

On multiple soliton similariton‐pair solutions, conservation laws via multiplier and stability analysis for the Whitham–Broer–Kaup equations in weakly dispersive media

Multiple Soliton Solutions of the Sawada-Kotera Equation with a Nonvanishing Boundary Condition and the Perturbed Korteweg de Vries Equation by Using the Multiple Exp-Function Scheme

Contact Info

Product

Resources

About