Novel distinct types of optical solitons for the coupled Fokas-Lenells equations

El-Shiekh, Rehab M.; Hamdy, Heba

doi:10.1007/s11082-023-04546-w

Cited by 14 publications

(3 citation statements)

References 33 publications

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“…Various methods, namely inverse scattering method, Hirota bilinearization and others (Lenells and Fokas, 2008;Matsuno, 2012b,a;Biswas et al, 2018b;Jawad et al, 2018;Krishnan et al, 2019;Biswas et al, 2018a;Aljohani et al, 2018;Onder et al, 2022;El-Shiekh and Hamdy, 2023;Gaballah et al, 2023;Cinar et al, 2022;Ullah et al, 2023) are proposed to obtain the different form of soliton solutions. In this manuscript our objective is to propose an alternate simplified and systematic scheme, namely bilinearization by introducing an auxiliary function and obtain a generalized expression for dark and bright dark soliton solutions.…”

Section: Introductionmentioning

confidence: 99%

Fokas-Lenells equation dark soliton and gauge equivalent spin equation

Dutta,

Talukdar,

Saharia

et al. 2023

Opt Quant Electron

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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.

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Section: Introductionmentioning

confidence: 99%

Fokas-Lenells equation dark soliton and gauge equivalent spin equation

Dutta,

Talukdar,

Saharia

et al. 2023

Opt Quant Electron

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“…( 1) is relatively a new equation and the study on this is going on in full swing. Many analytical approaches have been employed to derive soliton solutions of FLE (Biswas et al, 2018;Hosseini et al, 2020;Triki and Wazwaz, 2017;Baronio et al, 2015;Chen et al, 2018;Cinar et al, 2022;Onder et al, 2022;Ullah et al, 2023;Gomez S et al, 2022;El-Shiekh and Hamdy, 2023;Gaballah et al, 2023;Krishnan et al, 2019;Matsuno, 2012b,a;Talukdar et al, 2023). In general the works on FLE is done for constant dispersion and nonlinear coefficients.…”

Section: Introductionmentioning

confidence: 99%

Soliton Management for ultrashort pulse: dark and anti-dark solitons of Fokas-Lenells equation with a damping like perturbation and a gauge equivalent spin system

Dutta,

Saharia,

Talukdar

et al. 2024

Preprint

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We investigate the propagation of an ultrashort optical pulse using Fokas-Lenells equation (FLE) under varying dispersion, nonlinear effects and perturbation. Such a system can be said to be under soliton management (SM) scheme. At first, under a gauge transformation, followed by shifting of variables, we transform FLE under SM into a simplified form, which is similar to an equation given by Davydova and Lashkin for plasma waves, we refer to this form as DLFLE. Then, we propose a bilinearization for DLFLE in a non-vanishing background byintroducing an auxiliary function which transforms DLFLE into three bilinear equations. We solve these equations and obtain dark and anti-dark one-soliton solution (1SS) of DLFLE. From here, by reverse transformation of the solution, we obtain the 1SS of FLE and explore the soliton behavior under different SM schemes. Thereafter, we obtain dark and anti-dark two-soliton solution (2SS) of DLFLE and determine the shift in phase of the individual solitons on interaction through asymptotic analysis. We then, obtain the 2SS of FLE and represent the soliton graph for different SM schemes. Thereafter, we present the procedure to determine N-soliton solution (NSS) of DLFLE and FLE. Later, we introduce a Lax pair for DLFLE and through a gauge transformation we convert the spectral problem of our system into that of an equivalent spin system which is termed as Landau-Lifshitz (LL) system. LL equation (LLE) holds the potential to provide information about various nonlinear structures and properties of the system.

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“…Due to their wide applicability the study of optical solitons solutions are considered by professionals and academics, in recent years. Numerous significant methods have been put out, including motion of solitary waves in the nonlinear optics [21] , lipid sensor [22] , the analysis method [23] , generalized Jacobi elliptic expansion method [24] , the trial equation technique [25] , propagation of ultrashort optical pulses [26] , pulses propagation in nonlinear optical systems [27] , modulation instability criteria [28] , stability of solitons [29] , evolution of dark solitons [30] , intermodal dispersion effect [31] , and soliton solutions in birefringent optical fibre [32] . Soliton propagation dynamics through a fibre with maintained polarization are governed by the Radhakrishnan-Kundu-Lakshmanan equation (RKLE) which is a generalized version of the nonlinear Schrodinger's equation.…”

Section: Introductionmentioning

confidence: 99%

Optical soliton solutions of the coupled Radhakrishnan-Kundu-Lakshmanan equation by using the extended direct algebraic approach

Mahmood,

Srivastava,

Abbas

et al. 2023

Heliyon

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Novel distinct types of optical solitons for the coupled Fokas-Lenells equations

Cited by 14 publications

References 33 publications

Fokas-Lenells equation dark soliton and gauge equivalent spin equation

Fokas-Lenells equation dark soliton and gauge equivalent spin equation

Soliton Management for ultrashort pulse: dark and anti-dark solitons of Fokas-Lenells equation with a damping like perturbation and a gauge equivalent spin system

Optical soliton solutions of the coupled Radhakrishnan-Kundu-Lakshmanan equation by using the extended direct algebraic approach

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