Rogue wave solutions of a higher-order Chen–Lee–Liu equation

Zhang, Jing; Liu, Wei; Qiu, Deqin; Zhang, Yongshuai; Porsezian, K.; He, Jingsong

doi:10.1088/0031-8949/90/5/055207

Cited by 45 publications

(13 citation statements)

References 42 publications

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“…Without self‐phase modulation, Moses et al proved optical pulse propagation involving self‐steepening in 2007. This experiment well establishes the first experimental manifestation of the DNLSII equation . Alike the NLS equation, DNLSII equation is also a real physical model in optics.…”

Section: Introductionsupporting

confidence: 72%

“…Derivative nonlinear Schrödinger (DNLS)–type equations are significant nonlinear models that have many implementations in nonlinear optics fibers and plasma physics . In nonlinear optics, nonlinear effects are studied comprehensively.…”

Section: Introductionmentioning

confidence: 99%

“…In nonlinear optics, nonlinear effects are studied comprehensively. To describe the nonlinear effects in optical fibers without the inclusion of loss and gain, the nonlinear Schrödinger (NLS) equation is utilized . The employed NLS equation is a lowest‐order approximate model describing the nonlinear effects in optical fibers.…”

Section: Introductionmentioning

confidence: 99%

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A new numerical approach for single rational soliton solution of Chen‐Lee‐Liu equation with Riesz fractional derivative in optical fibers

Ray

2018

Math Methods in App Sciences

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In this paper, time-splitting spectral approximation technique has been proposed for Chen-Lee-Liu (CLL) equation involving Riesz fractional derivative. The proposed numerical technique is efficient, unconditionally stable, and of second-order accuracy in time and of spectral accuracy in space. Moreover, it conserves the total density in the discretized level. In order to examine the results, with the aid of weighted shifted Grünwald-Letnikov formula for approximating Riesz fractional derivative, Crank-Nicolson weighted and shifted Grünwald difference (CN-WSGD) method has been applied for Riesz fractional CLL equation. The comparison of results reveals that the proposed time-splitting spectral method is very effective and simple for obtaining single soliton numerical solution of Riesz fractional CLL equation. KEYWORDSChen-Lee-Liu equation, CN-WSGD method, Grünwald-Letnikov difference operator, Riesz fractional derivative, time-splitting spectral method, weighted shifted Grünwald-Letnikov formula | INTRODUCTIONAs a field of applied mathematics, fractional calculus is a generalization of the differentiation and integration of integer order to arbitrary order (real or complex order). The usefulness of fractional calculus has been found in various areas of science and engineering. Its application has been seen in many research areas such as transport processes, fluid dynamics, electrochemical processes, bioengineering, signal processing, control theory, fractal theory, porous media, viscoelastic materials, electrical circuits, plasma physics, and nuclear reactor kinetics. 1-7 Many physical and engineering phenomena, which are analyzed by fractional calculus, are considered to be best modeled by fractional differential equations (FDEs). During the past few decades, the intensive research pursuits in the development of the theory of FDEs have been experienced due to its capability to accurate elucidation of many real-life problems as the nature manifests in a fractional-order dynamical manner. Up to now, a great deal of effort has been devoted for solving the FDEs by various analytical and numerical methods. These methods include finite difference method, 8 operational matrix method, 9 (G ′ /G)-expansion method, 10-13 Adomian decomposition method, 14,15 differential transform method, 16,17 first integral method, 18,19 and fractional subequation method. 20,21 Derivative nonlinear Schrödinger (DNLS)-type equations are significant nonlinear models that have many implementations in nonlinear optics fibers and plasma physics. [22][23][24][25] In nonlinear optics, nonlinear effects are studied comprehensively. To describe the nonlinear effects in optical fibers without the inclusion of loss and gain, the nonlinear Schrödinger (NLS) equation is utilized. 22 The employed NLS equation is a lowest-order approximate model describing the nonlinear effects in optical fibers. Nowadays, higher-order nonlinear effects are inevitable in many optical systems

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Section: Introductionsupporting

confidence: 72%

Section: Introductionmentioning

confidence: 99%

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A new numerical approach for single rational soliton solution of Chen‐Lee‐Liu equation with Riesz fractional derivative in optical fibers

Ray

2018

Math Methods in App Sciences

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“…When r = q * , the compatibility condition yields the zero-curvature equation, U t −V x − [U,V ] = 0, which generates equation (1.3). The rogue wave solutions of the higher-order CLL equation were studied in [21] by using Darboux transformation method. The topic of the singular Riemann-Hilbert problem was very well researched between 1979 and 1984.…”

Section: Introductionmentioning

confidence: 99%

Riemann-Hilbert approach and N-soliton formula for a higher-order Chen-Lee-Liu equation

Hu¹,

Jian²,

Yu³

2021

JNMP

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We consider a higher-order Chen-Lee-Liu (CLL) equation with third order dispersion and quintic nonlinearity terms. In the framework of the Riemann-Hilbert method, we obtain the compact N-soliton formula expressed by determinants. Based on the determinant solution, some properties for single soliton and asymptotic analysis of N-soliton solution are explored. The simple elastic interaction of N solitons is confirmed.

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“…These models are considered under different circumstances such as dispersive solitons, differential group delay, and dispersion-managed solitons. Besides these familiar models, there is another class of versions of NLSE that is referred to as derivative NLSE (DNLSE) [27][28][29] that appears in three forms. One such form is the Chen-Lee-Liu equation [30][31][32] that incorporates higher order perturbations from optics and is going to be the focus of today's paper.…”

Section: Introductionmentioning

confidence: 99%

A Spectral Collocation Technique for Riesz Fractional Chen-Lee-Liu Equation

Abdelkawy

Alyami

2021

Journal of Function Spaces

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This paper discusses the study of optical solitons that are modeled by Riesz fractional Chen-Lee-Liu model, one of the versions of the famous nonlinear Schrödinger equation. This model is solved by the assistance of consecutive spectral collocation technique with two independent approaches. The first is the approach of the spatial variable, while the other is the approach of the temporal variable. It is concluded that the method of the current paper is far more efficient and credible for the proposed problem. Numerical results illustrate the performance efficiency of the algorithm. The results also point out that the scheme can lead to spectral accuracy of the studied model.

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Rogue wave solutions of a higher-order Chen–Lee–Liu equation

Cited by 45 publications

References 42 publications

A new numerical approach for single rational soliton solution of Chen‐Lee‐Liu equation with Riesz fractional derivative in optical fibers

A new numerical approach for single rational soliton solution of Chen‐Lee‐Liu equation with Riesz fractional derivative in optical fibers

Riemann-Hilbert approach and N-soliton formula for a higher-order Chen-Lee-Liu equation

A Spectral Collocation Technique for Riesz Fractional Chen-Lee-Liu Equation

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