Novel optical soliton solutions for time-fractional resonant nonlinear Schrödinger equation in optical fiber

Das, Nilkanta; Ray, S. Saha

doi:10.1007/s11082-021-03479-6

Cited by 23 publications

(3 citation statements)

References 33 publications

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“…Different types of phenomenon occurring chemically, biologically and economically, among others, are represented as non-linear partial differential equations (NLPDEs). Many different methods have been developed to gain the analytical wave solutions of these NLPDEs, i.e., the optical soliton solutions of coupled nonlinear Schrödinger equations have been gained with the use of the Kudryashov R function technique [13], some new kinds of optical soliton solutions of time-fractional perturbed nonlinear Schrödinger equations have been achieved by using the generalized Kudryashov scheme [14], by applying the modified auxiliary equation technique, optical wave solutions of time-fractional resonant non-linear Schrödinger equations have been obtained [15] and new optical wave solutions for time-fractional perturbed non-linear Schrödinger equations have been achieved by utilizing the improved tan(φ(ζ/2))-expansion scheme [16].…”

Section: Introductionmentioning

confidence: 99%

Discovery of New Exact Wave Solutions to the M-Fractional Complex Three Coupled Maccari’s System by Sardar Sub-Equation Scheme

Alsharidi

Bekir

2023

Symmetry

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In this paper, we succeed at discovering the new exact wave solutions to the truncated M-fractional complex three coupled Maccari’s system by utilizing the Sardar sub-equation scheme. The obtained solutions are in the form of trigonometric and hyperbolic forms. These solutions have many applications in nonlinear optics, fiber optics, deep water-waves, plasma physics, mathematical physics, fluid mechanics, hydrodynamics and engineering, where the propagation of nonlinear waves is important. Achieved solutions are verified with the use of Mathematica software. Some of the achieved solutions are also described graphically by 2-dimensional, 3-dimensional and contour plots with the help of Maple software. The gained solutions are helpful for the further development of a concerned model. Finally, this technique is simple, fruitful and reliable to handle nonlinear fractional partial differential equations (NLFPDEs).

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Section: Introductionmentioning

confidence: 99%

Discovery of New Exact Wave Solutions to the M-Fractional Complex Three Coupled Maccari’s System by Sardar Sub-Equation Scheme

Alsharidi

Bekir

2023

Symmetry

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“…Das and Saha Ray [42] established a novel optical soliton solution for time‐fractional resonant nonlinear Schrödinger equation in optical fiber. The same authors [43] applied a new optical soliton solution of fractional perturbed nonlinear Schrödinger equation in nanofibers.…”

Section: Introductionmentioning

confidence: 99%

An efficient wavelet‐based approximation method for solving nonlinear fractional‐time long wave equations: An operational matrix approach

Balaji,

Hariharan

2023

Math Methods in App Sciences

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This research paper develops an efficient Gegenbauer wavelet‐based approximation method to solve nonlinear fractional‐time regularized long wave (RLW) equations arising in ocean engineering. The operational matrices of derivatives, as well as the fractional order integration, are engaged in the proposed method. Using the operational matrix method and collocation point, the nonlinear RLW equations are converted into a system of algebraic equations, and these equations are further solved. Some results regarding the error‐bound estimation of this method have been developed. The method's accuracy and efficiency are confirmed by error estimation. The obtained results are compared with other available results and exact solutions. Moreover, the use of Gegenbauer wavelets is found to be a simple, straightforward forward and efficient tool for solving nonlinear PDEs arising in ocean engineering.

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“…Different types of phenomenon occurring chemically, biologically, economically and others are represented as a non-linear partial differential equations (NLPDEs). Many different methods are developed to gain the analytical wave solutions of these NLPDEs i.e optical soliton solutions of coupled nonlinear Schrödinger equation have been gained with the use of Kudryashov R function technique [1], some new kind of optical soliton solutions of time-fractional perturbed nonlinear Schrödinger equation have been achieved by using the generalized Kudryashov scheme [2], by applying the modified auxiliary equation technique, optical wave solutions of time-fractional resonant non-linear Schrödinger equation have been obtained [3], new optical wave solutions for the time-fractional perturbed non-linear Schrödinger equation have been achieved by utilizing the improved tan(φ(ζ/2))-expansion scheme [4].…”

Section: Introductionmentioning

confidence: 99%

Discovery of New ExactWave Solutions to the M-Fractional Complex Three Coupled Maccari’s System by Sardar Sub-Equation Scheme

Alsharidi¹,

Bekir²

2023

Preprint

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In this paper, we succeed to discover the new exact wave solutions to the truncated M-fractional complex three coupled Maccari’s system by utilizing the Sardar sub-equation scheme. The obtained solutions are in the form of trigonometric and hyperbolic forms. These solutions have many applications in nonlinear optics, fiber optics, deep water-waves, plasma physics, mathematical physics, fluid mechanics, hydrodynamics and engineering where the propagation of nonlinear waves is important. Achieved solutions are verified with the use of Mathematica software. Some of the achieved solutions are also described graphically by 2-dimensional, 3-dimensional and contour plots with the help of Maple software. The gained solutions are helpful for the further development of concerned model. Finally, this technique is simple, fruitful and reliable to handle the nonlinear FPDEs.

show abstract

Novel optical soliton solutions for time-fractional resonant nonlinear Schrödinger equation in optical fiber

Cited by 23 publications

References 33 publications

Discovery of New Exact Wave Solutions to the M-Fractional Complex Three Coupled Maccari’s System by Sardar Sub-Equation Scheme

Discovery of New Exact Wave Solutions to the M-Fractional Complex Three Coupled Maccari’s System by Sardar Sub-Equation Scheme

An efficient wavelet‐based approximation method for solving nonlinear fractional‐time long wave equations: An operational matrix approach

Discovery of New ExactWave Solutions to the M-Fractional Complex Three Coupled Maccari’s System by Sardar Sub-Equation Scheme

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