Optical soliton solutions to the Fokas–Lenells model applying the $${\boldsymbol{\varphi }}^{6}$$-model expansion approach

Seadawy, Aly R.; Ali, M. Zulfikar; Harun-Or-Roshid,

doi:10.1007/s11082-023-04771-3

Cited by 35 publications

(3 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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

View full text Add to dashboard Cite

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.

show abstract

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

View full text Add to dashboard Cite

show abstract

“…Consequently, the attraction of soliton solutions in the field of mathematical physics is considerable [ 7 , 8 ]. Many distinguished nonlinear models provide evidence of the presence of these soliton outcomes like the Jimbo-Miwa structure [ 9 ], Phi-4 equation [ 10 ], the extended Boussinesq nonlinear framework [ 11 ], the Nizhnik-Novikov-Veselov model [ 12 ], the ISLW system [ 13 ], the 3D fractional WBBM structure [ 14 ], Fokas-Lenells system [ 15 ], and various others [ 16 – 18 ]. Nonlinear models can be solved using a variety of effective methods, and soliton outcomes can be obtained.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation, chaos, and stability analysis to the second fractional WBBM model

Ullah,

Ali,

Roshid

2024

PLoS ONE

Self Cite

View full text Add to dashboard Cite

This manuscript investigates bifurcation, chaos, and stability analysis for a significant model in the research of shallow water waves, known as the second 3D fractional Wazwaz-Benjamin-Bona-Mahony (WBBM) model. The dynamical system for the above-mentioned nonlinear structure is obtained by employing the Galilean transformation to fulfill the research objectives. Subsequent analysis includes planar dynamic systems techniques to investigate bifurcations, chaos, and sensitivities within the model. Our findings reveal diverse features, including quasi-periodic, periodic, and chaotic motion within the governing nonlinear problem. Additionally, diverse soliton structures, like bright solitons, dark solitons, kink waves, and anti-kink waves, are thoroughly explored through visual illustrations. Interestingly, our results highlight the importance of chaos analysis in understanding complex system dynamics, prediction, and stability. Our techniques’ efficiency, conciseness, and effectiveness advance our understanding of this model and suggest broader applications for exploring nonlinear systems. In addition to improving our understanding of shallow water nonlinear dynamics, including waveform features, bifurcation analysis, sensitivity, and stability, this study reveals insights into dynamic properties and wave patterns.

show abstract

“…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

View full text Add to dashboard Cite

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).

show abstract

Optical soliton solutions to the Fokas–Lenells model applying the $${\boldsymbol{\varphi }}^{6}$$-model expansion approach

Cited by 35 publications

References 34 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

Bifurcation, chaos, and stability analysis to the second fractional WBBM model

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

Contact Info

Product

Resources

About