Optical soliton perturbation with Radhakrishnan–Kundu–Lakshmanan equation by Lie group analysis

Bansal, Anupma; Biswas, Anjan; Mahmood, Mohammad F.; Zhou, Qin; Mirzazadeh, Mohammad; Alshomrani, Ali Saleh; Moshokoa, Seithuti P.; Belić, Milivoj R.

doi:10.1016/j.ijleo.2018.02.104

Cited by 55 publications

(11 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(9). When we compare our results with the results reported in [40][41][42][43][44][45][46][47], we observed that, all the results obtained in this study by using the above method are newly structured solutions. These soliton solutions are located throughout parameter restrictions that provide their existence and novel soliton, traveling waves and kink-type solutions with complex structures while other solutions that emerged from the Laplace-Adomian decomposition method, traveling wave hypothesis, extended trial function scheme, among others.…”

Section: Resultssupporting

confidence: 59%

“…Moreover, some chirp-free bright optical soliton solutions of the model is presented by traveling wave hypothesis in [45]. Lie group analysis is also used in [46] to retrieve optical soliton solutions of the perturbed Radhakrishnan-Kundu-Lakshmanan equation. In [47], the authors investigated the conformable time-fractional perturbed RKL equation by utilizing the extended sinh-Gordon equation expansion method.…”

Section: V)mentioning

confidence: 99%

See 1 more Smart Citation

The generalized exponential rational function method for Radhakrishnan-Kundu-Lakshmanan equation with β-conformable time derivative

Ghanbari

Gómez-Aguilar

2019

Rev. Mex. Fís.

View full text Add to dashboard Cite

In this paper, the generalized exponential rational function method (GERFM) and the extended sinh-Gordon equation expansion method (ShGEEM) are used to construct exact solutions of the perturbed β-conformable-time Radhakrishnan-Kundu-Lakshmanan (RKL) equation. This model governs soliton propagation dynamics through a polarization-preserving fiber. Fractional derivatives are described in the β-conformable sense. As a result, we get new form of solitary traveling wave solutions for this model including novel soliton, traveling waves and kink-type solutions with complex structures. Physical interpretations of some extracted solutions are also included through taking suitable values of parameters and derivative order in them. It is proved that these methods are powerful, efficient, and can be fruitfully implemented to establish new solutions of nonlinear conformable-time partial differential equations applied in mathematical physics.

show abstract

Section: Resultssupporting

confidence: 59%

Section: V)mentioning

confidence: 99%

The generalized exponential rational function method for Radhakrishnan-Kundu-Lakshmanan equation with β-conformable time derivative

Ghanbari

Gómez-Aguilar

2019

Rev. Mex. Fís.

View full text Add to dashboard Cite

show abstract

“…Many researchers have recently developed exact solutions of SFRKLE (1), with σ = 0, using a variety of methods including trial equation method [41], Lie group analysis [42], sine-cosine method [43], first integral method [44], extended simple equation method [45], the modified Khater method [46], and improved tan ðϕðςÞ/2Þ-expansion method [47], while the analytical solutions of SFRKLE (1) have not yet been investigated.…”

Section: Introductionmentioning

confidence: 99%

The Analytical Solutions of the Stochastic Fractional RKL Equation via Jacobi Elliptic Function Method

Al‐Askar

Mohammed

2022

Advances in Mathematical Physics

View full text Add to dashboard Cite

This article considers the stochastic fractional Radhakrishnan-Kundu-Lakshmanan equation (SFRKLE), which is a higher order nonlinear Schrödinger equation with cubic nonlinear terms in Kerr law. To find novel elliptic, trigonometric, rational, and stochastic fractional solutions, the Jacobi elliptic function technique is applied. Due to the Radhakrishnan-Kundu-Lakshmanan equation’s importance in modeling the propagation of solitons along an optical fiber, the derived solutions are vital for characterizing a number of key physical processes. Additionally, to show the impact of multiplicative noise on these solutions, we employ MATLAB tools to present some of the collected solutions in 2D and 3D graphs. Finally, we demonstrate that multiplicative noise stabilizes the analytical solutions of SFRKLE at zero.

show abstract

“…In [2], authors studied bifurcations of exact travelling wave solutions for the generalized RKL equation. In [3], author obtained bright and dark soliton solutions for the Radhakrishnan-Kundu-Lakshmanan equation by Lie group analysis. In [4], authors established optical solitons of the RKE equation by the extended trial function integration scheme.…”

Section: Introductionmentioning

confidence: 99%

Optical solutions and other solutions for Radhakrishnan-Kundu-Laksmannan equation by using improved modified extended tanh-function method

Elsherbeny

Elbarkouky

Ahmed

et al. 2021

Preprint

View full text Add to dashboard Cite

This paper studies Radhakrishnan-Kundu-Laksmannan equation which is used to describe the pulse propagation in optical fiber communications. By using improved modified extended tanh-function method various types of solutions are extracted such as bright solitons, singular solitons, singular periodic wave solutions, Jacobi elliptic solutions, periodic wave solutions and Weierstrass elliptic doubly periodic solutions. Moreover, some of the obtained solutions are represented graphically.

show abstract

Optical soliton perturbation with Radhakrishnan–Kundu–Lakshmanan equation by Lie group analysis

Cited by 55 publications

References 6 publications

The generalized exponential rational function method for Radhakrishnan-Kundu-Lakshmanan equation with β-conformable time derivative

The generalized exponential rational function method for Radhakrishnan-Kundu-Lakshmanan equation with β-conformable time derivative

The Analytical Solutions of the Stochastic Fractional RKL Equation via Jacobi Elliptic Function Method

Optical solutions and other solutions for Radhakrishnan-Kundu-Laksmannan equation by using improved modified extended tanh-function method

Contact Info

Product

Resources

About