Optical soliton solutions for the coupled conformable Fokas–Lenells equation with spatio-temporal dispersion

Kallel, Wajdi; Almusawa, Hassan; Mirhosseini-Alizamini, Seyed Mehdi; Eslami, Mostafa; Rezazadeh, Hadi; Osman, M. S.

doi:10.1016/j.rinp.2021.104388

Cited by 39 publications

(7 citation statements)

References 41 publications

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“…Equation with Conformable Derivative Dependent on Time Parameter to find the Exact Dynamic Wave Solutions. The others feasible methods are the generalized Kudryashov method [36], the modified (𝐺 ′ 𝐺 ⁄ )-expansion method [37], the integration method [38], the modified symbolic computation method [39], the Hirota's bilinear operator's method [40], the tanh-function method [41]. Several researchers used the above mentioned (𝐺′ 𝐺 ⁄ )-expansion method to explore exact solution of different type of NLPDEs.…”

Section: Introductionmentioning

confidence: 99%

Discovering the innumerable solutions of the (1 +1 ) -dimensional integro-differential Ito and (2 + 1 ) -dimensional integro-differential Sawda-Kotera equations via an efficient analytical technique

Borhan

Miah

Iqbal

et al. 2023

Preprint

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This research work demonstrates an approach to solve nonlinear evolution equations via the generalized \(\left(G{\prime }/G\right)\)-expansion method which is an advantageous mathematical tool for establishing abundant solutions of these types of nonlinear evolution equations. Here, we select the \(\left(1+1\right)\)-dimensional integro-differential Ito equation and \(\left(2+1\right)\)-dimensional integro-differential Sawda-Kotera equation to extract the closed traveling wave solutions by using the mentioned method. In applied Mathematics, mathematical Physics, engineering science as well as real time application fields have enormous application of these type of equations. The new traveling wave solutions derived by this method are involving hyperbolic function, trigonometric function and rational function. This method is direct, efficient, convenient and powerful to solve other nonlinear evolution equations. Moreover, the features of the solutions are illustrated by some figures.

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Section: Introductionmentioning

confidence: 99%

Discovering the innumerable solutions of the (1 +1 ) -dimensional integro-differential Ito and (2 + 1 ) -dimensional integro-differential Sawda-Kotera equations via an efficient analytical technique

Borhan

Miah

Iqbal

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…Researchers are therefore motivated to present new methods and refine existing approaches. Various significant and powerful methods have been introduced such as Darboux transformation [14], Weierstrass elliptic functions methods [15,16], Bäcklund transformation [17], Lie group [18][19][20][21], Hirota's method [22,23], bifurcation method [24][25][26][27][28][29][30][31][32][33], and for distinct method, as shown in e.g., [34][35][36][37][38][39][40][41][42]. e analytical and numerical solutions for various types of nonlinear partial differential equations were investigated using traditional Lie symmetry approaches; for instance as shown in [43].…”

Section: Introductionmentioning

confidence: 99%

Integrability, Variational Principle, Bifurcation, and New Wave Solutions for the Ivancevic Option Pricing Model

Elmandouh

Elbrolosy

2022

Journal of Mathematics

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The Ivancevic option pricing model comes as an alternative to the Black-Scholes model and depicts a controlled Brownian motion associated with the nonlinear Schrodinger equation. The applicability and practicality of this model have been studied by many researchers, but the analytical approach has been virtually absent from the literature. This study intends to examine some dynamic features of this model. By using the well-known ARS algorithm, it is demonstrated that this model is not integrable in the Painlevé sense. He’s variational method is utilized to create new abundant solutions, which contain the bright soliton, bright-like soliton, kinky-bright soliton, and periodic solution. The bifurcation theory is applied to investigate the phase portrait and to study some dynamical behavior of this model. Furthermore, we introduce a classification of the wave solutions into periodic, super periodic, kink, and solitary solutions according to the type of the phase plane orbits. Some 3D-graphical representations of some of the obtained solutions are displayed. The influence of the model’s parameters on the obtained wave solutions is discussed and clarified graphically.

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“…Analogous to the derivation of the Camassa-Holm equation from the KdV equaiton [1], the FL equation was initially derived from the NLS equation by utilizing two Hamiltonian operators [2]. In optics, the FL equation characterizes the higher-order linear and nonlinear optical effects, and has been derived as a suitable model for the femtosecond pulse propagation through single mode optical silica fiber, for which several interesting solutions have been constructed [3][4][5].…”

Section: Introductionmentioning

confidence: 99%

A Riemann-Hilbert approach to existence of global solutions to the Fokas-Lenells equation on the line

Cheng¹,

Fan²

2022

Preprint

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We obtain the existence of global solutions to the Cauchy problem of the Fokas-Lenells (FL) equation on the linewhere without the small-norm assumption on initial data uOur main technical tool is the inverse scattering transform method based on the representation of a Riemann-Hilbert (RH) problem associated with the above Cauchy problem. The existence and the uniqueness of the RH problem is shown via a general vanishing lemma. The spectral problem associated with the FL equation is changed into an equivalent Zakharov-Shabat-type spectral problem to establish the RH problems on the real axis. By representing the solutions of the RH problem via the Cauchy integral protection and the reflection coefficients, the reconstruction formula is used to obtain a unique local solution of the FL equation. Further, the eigenfunctions and the reflection coefficients are shown Lipschitz continuous with respect to initial data, which provides a priori estimate of the solution to the FL equation. Based on the local solution and the uniformly priori estimate, we construct a unique global solution in H 3 (R) ∩ H 2,1 (R) to the FL equation.

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Optical soliton solutions for the coupled conformable Fokas–Lenells equation with spatio-temporal dispersion

Cited by 39 publications

References 41 publications

Discovering the innumerable solutions of the (1 +1 ) -dimensional integro-differential Ito and (2 + 1 ) -dimensional integro-differential Sawda-Kotera equations via an efficient analytical technique

Discovering the innumerable solutions of the (1 +1 ) -dimensional integro-differential Ito and (2 + 1 ) -dimensional integro-differential Sawda-Kotera equations via an efficient analytical technique

Integrability, Variational Principle, Bifurcation, and New Wave Solutions for the Ivancevic Option Pricing Model

A Riemann-Hilbert approach to existence of global solutions to the Fokas-Lenells equation on the line

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