The dynamic behaviors of the Radhakrishnan–Kundu–Lakshmanan equation by Jacobi elliptic function expansion technique

Tarla, Sibel; Ali, Karmina K.; Yılmazer, Reşat; Osman, M. S.

doi:10.1007/s11082-022-03710-y

Cited by 49 publications

(9 citation statements)

References 56 publications

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“…Jacobi elliptic functions have numerous applications in mathematical physics, including in the theory of elliptic integrals, the study of periodic solutions of nonlinear differential equations, and the analysis of periodic structures in materials science. The Jacobi elliptic function expansion method has been applied to a wide range of nonlinear partial differential equations [29][30][31][32][33][34][35][36][37][38]. The fundamental outline of JEFEM can be summarized as follows:…”

Section: Description Of the Jefemmentioning

confidence: 99%

“…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%

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

Tarla¹,

Ali²,

Yusuf³

2023

Phys. Scr.

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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.

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Section: Description Of the Jefemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Tarla¹,

Ali²,

Yusuf³

2023

Phys. Scr.

Self Cite

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“…Precise protracted predictions are unattainable with the existing technologies owing to this nonlinearity [4,5,6]. Various analytical methods have been utilized to solve different kinds of nonlinear equations, such as the extended direct algebraic method [7], the extended trial function method [8,9], the inverse scattering method [10], the Kudryashov expansion and sine-cosine method [11], the Jacobi elliptic function [12,13,14], modified generalized exponential rational function [15] and many others [16,17,18,19,20,21,22,23,24,25,26,27,29,30,31].…”

Section: Introductionmentioning

confidence: 99%

Optical solitons to the Perturbed Gerdjikov-Ivanov equation with quantic nonlinearity

et al. 2023

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In this article, we examine the Perturbed Gerdjikov-Ivanov equation by using the Jacobi elliptic function expansion method. This results in obtaining distinct solutions including dark, bright, singular solitons, periodic waves, singular periodic waves, and Jacobi elliptic function solutions. The 2-and 3-dimensional graphs of the reported solutions are presented. The reported results may be useful in explaining the physical features of the studied equation.

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“…The PDEs are an essential instrument for extensively investigating the features of physical processes [1][2][3][4]. The Schrödinger-type governing equation, which is critical in the disciplines of optics, fiber optics, mathematical physics, telecommunication engineering, and plasma technology, is one of the excellent ways to more accurately understand the complicated physical nonlinear model [5][6][7]. Due to the crucial role that exact solutions play in accurately representing the physical properties of nonlinear systems in applied mathematics, the derivation of analytical solutions for the Schrödinger and other water wave equations is a crucial study area [8][9][10][11][12][13][14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

New physical structures and patterns to the optical solutions of the nonlinear Schrödinger equation with a higher dimension

Ali

Yusuf

Alquran

et al. 2023

Commun. Theor. Phys.

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It is commonly recognized that, despite current analytical approaches, many physical aspects of nonlinear models remain unknown. It is critical to build more efficient integration methods in order to design and construct numerous other unknown solutions and physical attributes for the nonlinear models, as well as for the benefit of the largest audience feasible. To achieve this goal, we propose a new extended unified auxiliary equation technique, a brand-new analytical method for solving nonlinear PDEs. The proposed method is applied to the nonlinear Schrodinger equation with a higher dimension in the anomalous dispersion. Many interesting solutions have been obtained. Moreover, in order to shed more light on the features of the obtained solutions, the Figures for some obtained solutions are graphed. The propagation characteristics of the generated solutions are shown. The results show that the proper physical quantities and nonlinear wave qualities are connected to the parameter values. It is worth noting that the new method is really effective and efficient, and it may be applied to come up with a lot of novel solutions.

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The dynamic behaviors of the Radhakrishnan–Kundu–Lakshmanan equation by Jacobi elliptic function expansion technique

Cited by 49 publications

References 56 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

Optical solitons to the Perturbed Gerdjikov-Ivanov equation with quantic nonlinearity

New physical structures and patterns to the optical solutions of the nonlinear Schrödinger equation with a higher dimension

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