Exact wave solutions of the fourth order non-linear partial differential equation of optical fiber pulses by using different methods

Samir, Islam; Badra, Niveen; Seadawy, Aly R.; Ahmed, Hamdy M.; Arnous, Ahmed H.

doi:10.1016/j.ijleo.2021.166313

Cited by 58 publications

(7 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…expansion method [11,12], the Bernoulli subequation function method [13], the generalized exponential rational function method [14-16], the ¢ -( ) G 1 expansion method [17, 18], Hirota's simple method [19][20][21], and other methods [22][23][24][25][26][27] have been used to obtain solutions for these NPDEs. Additionally, the Jacobi elliptic function expansion method (JEFEM) has been applied to several NPDEs, including the Biswas-Arshed equation in [28], various nonlinear wave equations such as KdV, mKdV equations, Boussinesq model and nonlinear klein-gordon equation [29], the fourth-order NPDE and the Kaup-Newell equation in [30], and other related studies [31][32][33][34][35][36][37][38].Similarly, the new modification of the Sardar sub-equation method (MSSEM) has also been applied to several NPDEs such as the generalized unstable nonlinear Schrodinger equation in [39], the perturbed Fokas-Lenells equation in [40], the Korteweg-de Vries equation in [41], the Benjamin-Bona-Mahony equation and the Klein-Gordon equations in [42], the Klein-Fock-Gordon equation in [43], the Boussinesq equation in [44], the perturbed Gerdjikov-Ivanov equation in [45], and other related studies [46][47][48][49][50][51][52].…”

Section: Introductionmentioning

confidence: 99%

Retracted: Exploring new optical solutions for nonlinear Hamiltonian amplitude equation via two integration schemes

Tarla¹,

Ali²,

Yusuf³

2023

Phys. Scr.

View full text Add to dashboard Cite

This research explores the Jacobi elliptic expansion function method and a modified version of the Sardar sub-equation method to discover new exact solutions for the nonlinear Hamiltonian amplitude equation. {\color{blue}By applying these techniques, the study seeks to uncover previously unknown solutions for this equation, contributing to the understanding of its behavior and opening up new possibilities for its applications.} The solutions obtained using these methods are represented by hyperbolic, trigonometric, and exponential functions, and they include optical dark-bright, periodic, singular, and bright solutions. The dynamic behaviors of these solutions are demonstrated by selecting appropriate values for physical parameters. By assigning values to these parameters, the study aims to showcase how the solutions of the nonlinear Hamiltonian amplitude equation behave under different conditions. This analysis provides insights into the system's response and enables a deeper comprehension of its complex dynamics in various scenarios, contributing to the overall understanding of the equation's behavior and potential real-world implications. Overall, these methods are effective in analyzing and obtaining analytic solutions for nonlinear partial differential equations.

show abstract

Section: Introductionmentioning

confidence: 99%

Retracted: Exploring new optical solutions for nonlinear Hamiltonian amplitude equation via two integration schemes

Tarla¹,

Ali²,

Yusuf³

2023

Phys. Scr.

View full text Add to dashboard Cite

show abstract

“…Remark 1. In equation ( 8), the functions F, e, f , g, h satisfy the restricted relation (6) ( 7) and (8a-8d) mentioned in i 38 , if we select p ¼ r ¼ l ¼ 0, q ¼ 1, h ¼ F 0 F , this method turns to the G 0 G method [39][40][41][42][43][44] , if we select 46 and if we select…”

Section: The General Algebraic Methods (Gam)mentioning

confidence: 99%

Exact solutions for the conformable fractional coupled nonlinear Schrödinger equations with variable coefficients

Hong

2022

Journal of Low Frequency Noise, Vibration and Active Control

View full text Add to dashboard Cite

In this work, the general algebraic method is proposed for finding some solutions of a conformable fractional coupled nonlinear Schrödinger equation with variable coefficients arising in inhomogeneous fibers with two orthogonal polarization states. With the aid of symbolic computations, many types of new soliton pulse and periodic pulse solutions including complex doubly periodic solutions, solitary wave solutions, and trigonometric function solutions are obtained. Some 3D and 2D numerical simulations about these solutions are portraited, which show the novelty and visibility of the dynamical structure and propagation behavior of the corresponding model. Moreover, we found the W-shaped soliton pulse and the periodic wave pulse can be effectively controlled by changing the relative parameters of the frequency coefficients and orders, which will help us to have a better understanding about the internal structure of this model.

show abstract

“…In this section, some of the the obtained solutions are represented graphically for certain values of n, β, α, ν and a. Figure 1 shows 3D and 2D graphs of the bright soliton solution (24) for (n = 0.5, β = 1.34, α = 2.88, ν = 0.66, a = 0.7). Figure 2 shows 3D and 2D graphs of the singular periodic solution ( 25) for (n = 0.5, β = 3.08, α = −2.3, ν = 1.88, a = 2.72).…”

Section: Graphical Representation Of Some Solutionsmentioning

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

Self Cite

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

Exact wave solutions of the fourth order non-linear partial differential equation of optical fiber pulses by using different methods

Cited by 58 publications

References 17 publications

Retracted: Exploring new optical solutions for nonlinear Hamiltonian amplitude equation via two integration schemes

Retracted: Exploring new optical solutions for nonlinear Hamiltonian amplitude equation via two integration schemes

Exact solutions for the conformable fractional coupled nonlinear Schrödinger equations with variable coefficients

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

Contact Info

Product

Resources

About