W-shaped profile and breather-like soliton of the fractional nonlinear Schrödinger equation describing the polarization mode in optical fibers

Houwe, Alphonse; Abbagari, Souleymanou; Djorwé, Philippe; Saliou, Youssoufa; Doka, Serge Y.; İnç, Mustafa

doi:10.1007/s11082-022-03859-6

Cited by 12 publications

(2 citation statements)

References 48 publications

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“…Its significance in research drives the exploration of diverse forms of OSs. Multiple methodologies have been established to generate OS solutions for such models, including the modified (G′/G)-expansion method 8 – 10 , the unified method 11 , 12 , the modified double Laplace transform scheme 13 , the adapted exponential task scheme 14 , the symbolic computational approach 15 , generalized Riccati equation mapping 16 , mapping method 17 , the φ6-model expansion approach 18 , sine–Gordon expansion method 19 , the improved Kudryashov’s approach 20 , Lie symmetry analysis 21 , the New generalized auxiliary equation method 22 , binary Darboux transformations 23 , among many others.…”

Section: Introductionmentioning

confidence: 99%

Unveiling optical soliton solutions and bifurcation analysis in the space–time fractional Fokas–Lenells equation via SSE approach

Refaie Ali,

Alam,

Parven

2024

Sci Rep

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The space–time fractional Fokas–Lenells (STFFL) equation serves as a fundamental mathematical model employed in telecommunications and transmission technology, elucidating the intricate dynamics of nonlinear pulse propagation in optical fibers. This study employs the Sardar sub-equation (SSE) approach within the STFFL equation framework to explore uncharted territories, uncovering a myriad of optical soliton solutions (OSSs) and conducting a thorough analysis of their bifurcations. The discovered OSSs encompass a diverse array, including bright-dark, periodic, multiple bright-dark solitons, and various other types, forming a captivating spectrum. These solutions reveal an intricate interplay among bright-dark solitons, complex periodic sequences, rhythmic breathers, coexistence of multiple bright-dark solitons, alongside intriguing phenomena like kinks, anti-kinks, and dark-bell solitons. This exploration, built upon meticulous literature review, unveils previously undiscovered wave patterns within the dynamic framework of the STFFL equation, significantly expanding the theoretical understanding and paving the way for innovative applications. Utilizing 2D, contour, and 3D diagrams, we illustrate the influence of fractional and temporal parameters on these solutions. Furthermore, comprehensive 2D, 3D, contour, and bifurcation analysis diagrams scrutinize the nonlinear effects inherent in the STFFL equation. Employing a Hamiltonian function (HF) enables detailed phase-plane dynamics analysis, complemented by simulations conducted using Python and MAPLE software. The practical implications of the discovered OSS solutions extend to real-world physical events, underlining the efficacy and applicability of the SSE scheme in solving time–space nonlinear fractional differential equations (TSNLFDEs). Hence, it is crucial to acknowledge the SSE technique as a direct, efficient, and reliable numerical tool, illuminating precise outcomes in nonlinear comparisons.

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Section: Introductionmentioning

confidence: 99%

Unveiling optical soliton solutions and bifurcation analysis in the space–time fractional Fokas–Lenells equation via SSE approach

Refaie Ali,

Alam,

Parven

2024

Sci Rep

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“…The FL equation has enormous applications in fiber-optics communication, is vital in investigation and therefore the search for diverse forms of OSs is very substantial. Numerous approaches have been established for creating OS solutions for such models, including modified (G'/G)-expansion method [8,9,10], the unified method [11,12], modified double Laplace transform scheme [13], the adapted exponential task scheme [14], The symbolic computational approach [15], generalized Riccati equation mapping [16], mapping method [17], the φ6 -model expansion approach [18], sineGordon expansion method [19], the improved Kudryashov's approach [20], Lie symmetry analysis [21], New generalized auxiliary equation method [22], binary darboux transformations [23] and so many.…”

Section: Introductionmentioning

confidence: 99%

Exploring Optical Soliton Solutions and Bifurcation Analysis in the Space- Time Fractional Fokas-Lenells (STFFL) Equation with Sardar Sub-Equation (SSE) Approach

Ali,

Alam,

Parven

2023

Preprint

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The space-time fractional Fokas-Lenells (STFFL) equation is a mathematical model used in telecommunications and transmission technology to describe complex phenomena. It explains nonlinear pulse propagation in optical fibers. In this study, we use the Sardar sub-equation (SSE) approach with the STFFL equation to find unexplored optical soliton solutions (OSSs) and analyze their bifurcations. These OSSs include bright-dark, periodic, multiple bright-dark solitons, and various types. We use 2D, contour, and 3D diagrams to illustrate the impact of fractional and time parameters on these solutions. Additionally, we create 2D, 3D, contour, and bifurcation analysis diagrams to examine the nonlinear effects of the STFFL equation. We establish a Hamiltonian function (HF) for phase plane dynamics analysis and conduct simulations using Python and MAPLE software. The discovered OSS solutions have practical implications for real-world physical events. This study demonstrates the utility and reliability of the SSE scheme for solving time-space nonlinear fractional differential equations (TSNLFDEs).

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Instability modulation and novel optical soliton solutions to the Gerdjikov–Ivanov equation with M-fractional

2023

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W-shaped profile and breather-like soliton of the fractional nonlinear Schrödinger equation describing the polarization mode in optical fibers

Cited by 12 publications

References 48 publications

Unveiling optical soliton solutions and bifurcation analysis in the space–time fractional Fokas–Lenells equation via SSE approach

Unveiling optical soliton solutions and bifurcation analysis in the space–time fractional Fokas–Lenells equation via SSE approach

Exploring Optical Soliton Solutions and Bifurcation Analysis in the Space- Time Fractional Fokas-Lenells (STFFL) Equation with Sardar Sub-Equation (SSE) Approach

Instability modulation and novel optical soliton solutions to the Gerdjikov–Ivanov equation with M-fractional

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