Fokas-Lenells equation dark soliton and gauge equivalent spin equation

Dutta, Riki; Talukdar, Sagardeep; Saharia, Gautam K.; Nandy, Sudipta

doi:10.1007/s11082-023-05460-x

Cited by 4 publications

(3 citation statements)

References 39 publications

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“…And this will also lead to a restriction |p 1r | ≤ κ 3 ρ 2 (1 + κρ 2 ). It is interesting to point out that in case of D(τ ) = R(τ ) = 1, the obtained expressions for g, f align with the results already deduced for DLFLE having constant coefficients (Dutta et al, 2023), which is expected.…”

Section: Dark and Anti-dark 1sssupporting

confidence: 84%

“…Eventually, we obtain the 2SS of FLE. In our previous paper (Dutta et al, 2023), we had implemented an analogous scheme to realize soliton solution of FLE (DLFLE form to be precise), but for constant coefficients (D(t) = R(t) = 1) and now we extend the scheme to realize the soliton of FLE under SM (Eqn. (2)).…”

Section: Introductionmentioning

confidence: 99%

“…(2)). Again, it is observed that various nonlinear equations show gauge equivalence with spin system equations (referred as LLE) (Takhtajan and Zakharov, 1979;Kundu, 1984;, even DLFLE having D(t) = R(t) = 1 shows gauge equivalent LLE (Dutta et al, 2023). LLE can provide interesting features about a system which are important from physical and mathematical point of view (Lakshmanan, 2011;Guo and Ding, 2008).…”

Section: Introductionmentioning

confidence: 99%

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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

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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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Section: Dark and Anti-dark 1sssupporting

confidence: 84%

Section: Introductionmentioning

confidence: 99%