Bell and kink type soliton solutions in birefringent nano-fibers

Ali, Kashif; Rizvi, Syed T. R.; Ahmad, Shamim; Bashir, Seemab; Younis, Muhammad

doi:10.1016/j.ijleo.2017.06.014

Cited by 17 publications

(5 citation statements)

References 22 publications

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“…More complicated calculations have been done using Maple, to acquire the unidentified constants. Substituting (14) into 3, equaling the coefficients of , , , and to zero, and solving the resulting nonlinear algebraic system (up to 150 equations), we explore the following solution cases of the constant parameters. In each case, we do back substitution in (14).…”

Section: Lump Solitons With Tough Waves (Two-stripe Solitons)mentioning

confidence: 99%

“…However, some problems occur in applying those methods, such as how to find Lax pairs in the DT method and how to carry out the back-substitution procedure in the LS method. There are also new types of closed-form solutions, for example, positions and complexions [4][5][6][7][8], and even new collision phenomena including fissions and fusions [9][10][11][12][13][14]. The Hirota bilinear method plays an influential role in discovering all the mentioned types of solutions to overcome a lot of analytic problems.…”

Section: Introductionmentioning

confidence: 99%

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Abundant Lump-Type Solutions and Interaction Solutions for a Nonlinear (3+1) Dimensional Model

Sadat

Kassem

2018

Advances in Mathematical Physics

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We explore dynamical features of lump solutions as diversion and propagation in the space. Through the Hirota bilinear method and the Cole-Hopf transformation, lump-type solutions and their interaction solutions with one- or two-stripe solutions have been generated for a generalized (3+1) shallow water-like (SWL) equation, via symbolic computations associated with three different ansatzes. The analyticity and localization of the resulting solutions in the (x,y,z, and t) space have been analyzed. Three-dimensional plots and contour plots are made for some special cases of the solutions to illustrate physical motions and peak dynamics of lump soliton waves in higher dimensions. The study of lump-type solutions moderates the visuality of optics media and oceanography waves.

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Section: Lump Solitons With Tough Waves (Two-stripe Solitons)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Abundant Lump-Type Solutions and Interaction Solutions for a Nonlinear (3+1) Dimensional Model

Sadat

Kassem

2018

Advances in Mathematical Physics

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“…In recent times, since solving NLSEs has attracted great interest of researchers, a wide range of analytical methods have been put forward in the literature to solve them. The analytical methods proposed encompass a broad range of approaches, including but not limited to the unified Riccati equation expansion [35,36], F-expansion [37], Fan's method [38], Kudryashov methods [12,[39][40][41][42], exp-function [43], G ′ /G-expansion method [44], sine-Gordon expansion method [45], extended sinh-Gordon equation [46,47], the modified extended tanh function [48], and many more [49][50][51]. The dimensionless form of the Biswas-Milovic equation (BME) was introduced as follows [10]:…”

Section: Introductionmentioning

confidence: 99%

Optical solitons of a perturbed Biswas-Milovic equation with parabolic-law nonlinearity and spatio-temporal dispersion

Çinar

2023

Preprint

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This paper deals with a new variant of the Biswas-Milovic equation, referred to as the perturbed Biswas-Milovic equation with parabolic-law nonlinearity in spatio-temporal dispersion. To our best knowledge, the considered equation which models the pulse propagation in optical fiber is studied for the first time, and the abundant optical solitons are successfully obtained utilizing the auxiliary equation method. Furthermore, we also investigate the impact of the parameters such as the spatio-temporal dispersion and the parabolic nonlinearity on the behavior of the soliton. The auxiliary equation method was employed due to its effectiveness in extracting abundant and diverse kinds of soliton solutions, including bright, kink, and singular. It has been tested and verified using Mathematica that all solutions obtained satisfy the main equation. 3D, 2D, and contour graphs of the solution functions are plotted and interpreted to understand the physical behavior of the model. The new model and findings may contribute to the understanding and characterization of the nonlinear behavior of pulse propagation in optical fibers, which is crucial for the development of optical communication systems.

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“…In recent times, since solving NLSEs has attracted great interest of researchers, a wide range of analytical methods have been put forward in the literature to solve them. The analytical methods proposed encompass a broad range of approaches, including but not limited to the unified Riccati equation expansion [36,37], F-expansion [38], Fan's method [39], Kudryashov methods [12,[40][41][42][43], exp-function [44], G ′ /G-expansion method [45], sine-Gordon expansion method [46], extended sinh-Gordon equation [47,48], the modified extended tanh function [49], and many more [50][51][52]. The dimensionless form of the Biswas-Milovic equation (BME) was introduced as follows [10]:…”

Section: Introductionmentioning

confidence: 99%

Explicit optical solitons of a perturbed Biswas-Milovic equation having parabolic-law nonlinearity and spatio-temporal dispersion

CINAR

2023

Preprint

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Objective – This paper deals with a new variant of the Biswas-Milovic equation, referred to as the perturbed Biswas-Milovic equation with parabolic-law nonlinearity in spatio-temporal dispersion. To our best knowledge, the considered equation which models the pulse propagation in optical fiber is studied for the first time, and the abundant optical solitons are successfully obtained utilizing the auxiliary equation method. Methods – Utilizing a wave transformation technique on the considered Biswas-Milovic equation, and by distinguishing its real and imaginary components, we have been able to restructure the considered equation into a set of nonlinear ordinary differential equations. The solutions for these ordinary differential equations, suggested by the auxiliary equation method, include certain undetermined parameters. These solutions are then incorporated into the nonlinear ordinary differential equation, leading to the formation of an algebraic equation system by collecting like terms of the unknown function and setting their coefficients to zero. The undetermined parameters, and consequently the solutions to the Biswas-Milovic equation, are derived by resolving this system. Results – 3D, 2D, and contour graphs of the solution functions are plotted and interpreted to understand the physical behavior of the model. Furthermore, we also investigate the impact of the parameters such as the spatio-temporal dispersion and the parabolic nonlinearity on the behavior of the soliton. Conclusion – The new model and findings may contribute to the understanding and characterization of the nonlinear behavior of pulse propagation in optical fibers, which is crucial for the development of optical communication systems.

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Bell and kink type soliton solutions in birefringent nano-fibers

Cited by 17 publications

References 22 publications

Abundant Lump-Type Solutions and Interaction Solutions for a Nonlinear (3+1) Dimensional Model

Abundant Lump-Type Solutions and Interaction Solutions for a Nonlinear (3+1) Dimensional Model

Optical solitons of a perturbed Biswas-Milovic equation with parabolic-law nonlinearity and spatio-temporal dispersion

Explicit optical solitons of a perturbed Biswas-Milovic equation having parabolic-law nonlinearity and spatio-temporal dispersion

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