Dynamical behaviors of various optical soliton solutions for the Fokas–Lenells equation

Hendi, Awatif A.; Ouahid, Loubna; Kumar, Sachin; Owyed, Saud; Abdou, M. A.

doi:10.1142/s0217984921505291

Cited by 26 publications

(7 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…While the study on NLSE, HNLSE and DNLSE is done extensively, the study on FLE is relatively sparse. A few of the recent notable contributions on FLE are solitary wave and elliptical solutions of FLE in presence of perturbation and modulation instability (Arshad et al, 2019), combined optical solitary waves of FLE (Triki and Wazwaz, 2017), dynamical behaviour of soliton solutions of FLE (Hendi et al, 2021), inverse transform of FLE with non zero boundary condition (Zhao and Fan, 2021), derivation of solitons of dimensionless FLE with perturbation term (Cinar et al, 2022) and more.…”

Section: Introductionmentioning

confidence: 99%

Fokas-Lenells equation dark soliton and gauge equivalent spin equation

Dutta,

Talukdar,

Saharia

et al. 2023

Opt Quant Electron

View full text Add to dashboard Cite

We propose the Hirota bilinearization of the Fokas-Lenells derivative nonlinear Schrödinger equation with a non-vanishing background. The bilinear method is applied using an auxilary function to obtain the dark one soliton solution, dark two soliton solution and eventually the scheme for obtaining dark N soliton solutions. The use of auxilary function in bilinearization makes the method simpler than the ones reported earlier. Later, we have introduced a Lax pair for this integrable equation and using a transformation we have shown that this system is gauge equivalent to a spin system, namely the Landau-Lifshitz equation.

show abstract

Section: Introductionmentioning

confidence: 99%

Fokas-Lenells equation dark soliton and gauge equivalent spin equation

Dutta,

Talukdar,

Saharia

et al. 2023

Opt Quant Electron

View full text Add to dashboard Cite

show abstract

“…When compensating from Equations ( 8)- (10) into Equations ( 1) and (2), with the separation of the real and imaginary parts, we obtain:…”

Section: Stochastic Solitons and Other Solutionsmentioning

confidence: 99%

Stochastic Solitons in Birefringent Fibers for Biswas–Arshed Equation with Multiplicative White Noise via Itô Calculus by Modified Extended Mapping Method

2023

View full text Add to dashboard Cite

Stochastic partial differential equations have wide applications in various fields of science and engineering. This paper addresses the optical stochastic solitons and other exact stochastic solutions through birefringent fibers for the Biswas–Arshed equation with multiplicative white noise using the modified extended mapping method. This model contains many kinds of soliton solutions, which are always symmetric or anti-symmetric in space. Stochastic bright soliton solutions, stochastic dark soliton solutions, stochastic combo bright–dark soliton solutions, stochastic combo singular-bright soliton solutions, stochastic singular soliton solutions, stochastic periodic solutions, stochastic rational solutions, stochastic Weierstrass elliptic doubly periodic solutions, and stochastic Jacobi elliptic function solutions are extracted. The constraints on the parameters are considered to guarantee the existence of these stochastic solutions. Furthermore, some of the selected solutions are described graphically to demonstrate the physical nature of the obtained solutions.

show abstract

“…The mentioned system can be used to describe the dynamic features of optical and photonic crystal fibers [29]. To express soliton solutions, the Fokas-Lenells PDE has been studied by applying numerous reliable and effective elegant algorithms, such as the Ricati equation scheme [30], extended trial equation scheme [31], complex envelope function ansatz [29], mapping scheme [32], unified solver method [33], φ 6 -model expansion approach [34], etc.…”

Section: Introductionmentioning

confidence: 99%

New wave behaviors of the Fokas-Lenells model using three integration techniques

Ullah,

Roshid,

Ali

2023

PLoS ONE

View full text Add to dashboard Cite

In this investigation, we apply the improved Kudryashov, the novel Kudryashov, and the unified methods to demonstrate new wave behaviors of the Fokas-Lenells nonlinear waveform arising in birefringent fibers. Through the application of these techniques, we obtain numerous previously unreported novel dynamic optical soliton solutions in mixed hyperbolic, trigonometric, and rational forms of the governing model. These solutions encompass periodic waves with W-shaped profiles, gradually increasing amplitudes, rapidly increasing amplitudes, double-periodic waves, and breather waves with symmetrical or asymmetrical amplitudes. Singular solitons with single and multiple breather waves are also derived. Based on these findings, we can say that our implemented methods are more reliable and useful when retrieving optical soliton results for complicated nonlinear systems. Various potential features of the derived solutions are presented graphically.

show abstract

Dynamical behaviors of various optical soliton solutions for the Fokas–Lenells equation

Cited by 26 publications

References 41 publications

Fokas-Lenells equation dark soliton and gauge equivalent spin equation

Fokas-Lenells equation dark soliton and gauge equivalent spin equation

Stochastic Solitons in Birefringent Fibers for Biswas–Arshed Equation with Multiplicative White Noise via Itô Calculus by Modified Extended Mapping Method

New wave behaviors of the Fokas-Lenells model using three integration techniques

Contact Info

Product

Resources

About