Optical soliton solutions for the integrable Lakshmanan-Porsezian-Daniel equation via the inverse scattering transformation method with applications

Ali, Mohamed R.; Khattab, Mahmoud A.; Mabrouk, S. M.

doi:10.1016/j.ijleo.2022.170256

Cited by 24 publications

(8 citation statements)

References 51 publications

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“…Based on expression (4) and equation (11), we find the other one Auto-Bäcklund transformation for equation (1):…”

Section: U H B U H B U H B U H H B H U B H U U B H U B H U B U B H U ...mentioning

confidence: 99%

“…Then, a number of new solutions to equation (1) from equation ( 12) can be found by solving equation (11).…”

Section: U H B U H B U H B U H H B H U B H U U B H U B H U B U B H U ...mentioning

confidence: 99%

“…And a large number of solutions of NLEEs with different forms such as rogue wave and lump wave solutions [4] are studied. Some methods have been proposed by scientists to study analytic solutions of NLEEs, such as Darboux transformation [5,6], the Hirota bilinear method [7][8][9][10], the inverse scattering method [11], Bäcklund transformation [12,13], exp-function method [14,15]and other methods [16][17][18].…”

Section: Introductionmentioning

confidence: 99%

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Complexiton solutions, kink soliton and breather-wave solutions for the (2+1)-dimensional combined potential Kadomtsev-Petviashvili with B-type Kadomtsev-Petviashvili equation

Ma,

Su,

Deng

2023

Phys. Scr.

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In this paper, the (2+1)-dimensional combined potential Kadomtsev-Petviashvili with B-type Kadomtsev-Petviashvili equation is an object of the research. Based on the extended homogeneous balancing method, Auto-B$\rm{\ddot a}$cklund transformations are obtained in two cases. Subsequently, with the help of these transformations, we obtain various explicit solutions of this equation. We attain complexiton solutions consisting of exponential, hyperbolic and trigonometric solutions from the Hirota bilinear form of this equation through the extended transformed rational function method. Also, we derive one-kink and two-kink soliton solutions by Maple symbolic calculation and the breather-wave solution via the extended homoclinic test approach. In addition, 3D graphics and density plots of the obtained solutions are depicted to illustrate the dynamical features of these solutions

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“…Based on expression (4) and equation (11), we find the other one Auto-Bäcklund transformation for equation (1):…”

Section: U H B U H B U H B U H H B H U B H U U B H U B H U B U B H U ...mentioning

confidence: 99%

“…Then, a number of new solutions to equation (1) from equation ( 12) can be found by solving equation (11).…”

Section: U H B U H B U H B U H H B H U B H U U B H U B H U B U B H U ...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Complexiton solutions, kink soliton and breather-wave solutions for the (2+1)-dimensional combined potential Kadomtsev-Petviashvili with B-type Kadomtsev-Petviashvili equation

Ma,

Su,

Deng

2023

Phys. Scr.

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“…The study of systems that can be precisely solved using analytical techniques is the focus of the field of integrable systems, which includes the Darboux transformation as a key tool. It has played a central role in the development of many important mathematical concepts, such as soliton theory and the inverse scattering method [28][29][30].…”

Section: Introductionmentioning

confidence: 99%

A Soliton Solution for the Kadomtsev–Petviashvili Model Using Two Novel Schemes

et al. 2023

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Symmetries are crucial to the investigation of nonlinear physical processes, particularly the evaluation of a differential problem in the real world. This study focuses on the investigation of the Kadomtsev–Petviashvili (KP) model within a (3+1)-dimensional domain, governing the behavior of wave propagation in a medium characterized by both nonlinearity and dispersion. The inquiry employs two distinct analytical techniques to derive multiple soliton solutions and multiple solitary wave solutions. These methods include the modified Sardar sub-equation technique and the Darboux transformation (DT). The modified Sardar sub-equation technique is used to obtain multiple soliton solutions, while the DT is introduced to develop two bright and two dark soliton solutions. These solutions are presented alongside their corresponding constraint conditions and illustrated through 3-D, 2-D, and contour plots to physically portray the derived solutions. The results demonstrate that the employed analytical techniques are useful and have not yet been explored in the context of the analyzed models. The proposed methodologies are valuable and can be applied to additional nonlinear evolutionary models employed to describe nonlinear physical models within the domain of nonlinear science.

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“…Because optical soliton provides an NLSE solution [28,36], it is critical to obtain its exact solutions [1,6]. There are various ways for studying, analyzing, and solving NLSE [19,27], including the Hirota bilinear approach [25], inverse scaling transformation [4], homogeneous balancing scheme [14], Darboux transformation method [18], function expansion approach [24] and many other methods. However, the optical solitons generated by various methods offer distinct benefits and disadvantages in their characteristics.…”

Section: Introductionmentioning

confidence: 99%

Dynamical Discussion and Diverse Soliton Solutions via Complete Discrimination System Approach Along with Bifurcation Analysis for the Third Order NLSE

Rizvi,

Seadawy,

Mustafa

2023

MJMS

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The purpose of this study is to introduce the wave structures and dynamical features of the third-order nonlinear Schr\"{o}dinger equations (TONLSE). We take the original equation and, using the traveling wave transformation, convert it into the appropriate traveling wave system, from which we create a conserved quantity known as the Hamiltonian. The Jacobian elliptic function solution (JEF), the hyperbolic function solution, and the trigonometric function solution are just a few of the optical soliton solutions to the equation that may be found using the complete discrimination system (CDS) of polynomial method (CDSPM) and also transfer the JEF into solitary wave (SW) soltions. It also includes certain dynamic results, such as bifurcation points and critical conditions for solutions, that might be utilized to explore the dynamic features of the equation employing the CDSPM. This method could also be used for qualitative analysis. The qualitative analysis is used to illustrate the equilibrium points and phase potraits of the equation. Phase portraits are visual representations used in dynamical systems to illustrate a system's behaviour through time. They can provide crucial information about a system's stability, periodic behaviour, and the presence of attractors or repellents.

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Optical soliton solutions for the integrable Lakshmanan-Porsezian-Daniel equation via the inverse scattering transformation method with applications

Cited by 24 publications

References 51 publications

Complexiton solutions, kink soliton and breather-wave solutions for the (2+1)-dimensional combined potential Kadomtsev-Petviashvili with B-type Kadomtsev-Petviashvili equation

Complexiton solutions, kink soliton and breather-wave solutions for the (2+1)-dimensional combined potential Kadomtsev-Petviashvili with B-type Kadomtsev-Petviashvili equation

A Soliton Solution for the Kadomtsev–Petviashvili Model Using Two Novel Schemes

Dynamical Discussion and Diverse Soliton Solutions via Complete Discrimination System Approach Along with Bifurcation Analysis for the Third Order NLSE

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