Exploring soliton solutions to sixth order dispersive non-linear Schrödinger equation with Kerr law nonlinearity using modified extended direct algebraic method

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

doi:10.1007/s11082-022-04459-0

Cited by 8 publications

(3 citation statements)

References 38 publications

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“…On the other hand, the nonlinear Schrödinger equations (NLSEs) are an important class of NLEEs that are widely used to model many physical phenomena in engineering and science [54–57]. Many researchers have studied and solved NLSE and its generalizations by using different techniques such as modified tanh expansion method which has been applied to study Biswas and Arshed equation having nonlinearity

n

while the semi‐inverse variational scheme has been used to extract different types of bright solitons for perturbed Gerdjikov–Ivanov (GI) equation [58, 59].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of optical solitons in the extended (3+1)‐dimensional nonlinear conformable Kudryashov equation with generalized anti‐cubic nonlinearity

Mirzazadeh,

Hashemi,

Akbulu

et al. 2024

Math Methods in App Sciences

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The nonlinear Schrödinger equation (NLSE) is a fundamental equation in the field of nonlinear optics and plays an important role in the study of many physical phenomena. The present study introduces a new model that demonstrates the novelty of the paper and provides the advancement of knowledge in the area of nonlinear optics by solving a challenging problem known as the extended ‐dimensional nonlinear conformable Kudryashov's equation (CKE) with generalized anti‐cubic nonlinearity, which is a generalization of the NLSE to three spatial dimension and one temporal dimension for the first time. This work is significant because it advances our understanding of nonlinear optics and its applications to solve complex equations in physics and related disciplines. The extended hyperbolic function method (EHFM) and Nucci's reduction method are applied to the extended ‐dimensional nonlinear CKE with generalized anti‐cubic nonlinearity. The equation is solved by using the concept of conformable derivative, a recently developed operator in fractional calculus, which has advantages over other fractional derivatives in terms of accuracy and flexibility. The attained solutions include periodic singular, dark 1‐soliton, singular 1‐soliton, and bright 1‐soliton which are visualized using 3D and contour plots. This study highlights the potential of using conformable derivative and the applied techniques to solve complex nonlinear differential equations in various fields. The obtained solutions and analysis will be useful in the design and analysis of optical communication systems and other related fields. Overall, this study contributes for the understanding of the dynamics of the extended ‐dimensional nonlinear CKE and offers new insights into the use of mathematical techniques to tackle complex problems in physics and related fields.

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while the semi‐inverse variational scheme has been used to extract different types of bright solitons for perturbed Gerdjikov–Ivanov (GI) equation [58, 59].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of optical solitons in the extended (3+1)‐dimensional nonlinear conformable Kudryashov equation with generalized anti‐cubic nonlinearity

Mirzazadeh,

Hashemi,

Akbulu

et al. 2024

Math Methods in App Sciences

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“…Owing to its broad practical backgrounds, nonlinear science is of important practical applications and theoretical research significance in mathematics. As one kind of the important mathematical models, nonlinear evolution equation can describe a lot of phenomena, such as fluid mechanics, optics, dynamics, solid state physics, plasma physics [1][2][3][4][5], etc. In recent years, there have been many methods to study the integrability and nonlinear localized waves of the nonlinear evolution equation, e.g., the Hirota bilinear method [6,7], Darboux transformation [8][9][10], Bäcklund transformation [11,12], inverse scattering method [13,14], and so on [15].…”

Section: Introductionmentioning

confidence: 99%

Solitons, lump and interactional solutions of the (3+1)-dimensional BLMP equation in incompressible fluid

He,

Han,

et al. 2024

Phys. Scr.

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Based on the Hirota bilinear method, we systematically investigate the (3+1)-dimensional Boiti-Leon-Manana-Pempinelli (BLMP) equation in incompressible fluids and main results include: (1) the formulas of N-kink-soliton solutions and the bound states of multi solitons are all presented, (2) the lump solution is derived by the positive quadratic function method, (3) the interactional solutions are given, i.e., one lump interacts with one- and two-kink-soliton, (4) some special periodic solutions are discussed, i.e., lump-periodic solutions and homoclinic breather solutions.

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“…Studying the nature of the propagated wave through fibers is very necessary to enhance the performance and the stability of network communications. Many models are employed to describe the wave nature via optical fibers like non-linear Schrödinger (NLS) model [14], Chen-Lee-Liu model [15,16], Gerdjikov-Ivanov model [2] and Biswas-Arshed equation [17,18]. Recently, it has become generally recognized in a variety of fields how important it is to consider random effects when predicting, modeling, simulating, and analyzing physical phenomena [19].…”

Section: Introductionmentioning

confidence: 99%

Propagation wave solutions with non-local nonlinearityfor stochastic NLSE

Alhojilan

Samir

2023

Preprint

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In this research article, the stochastic nonlinear Schr¨odinger equation (NLSE) with non-local nonlinearity is considered. This model is used to mimic the wave propagation through optical fibers. Theintegration technique of the improved modified extended tanh scheme is implemented to handle theinvestigated model. Many stochastic solutions are raised such as bright solitons, dark and singular solitons. 3D and 2D visualizations are introduced with different noise intensities to show the robust of theextracted solutions against the noise.

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Exploring soliton solutions to sixth order dispersive non-linear Schrödinger equation with Kerr law nonlinearity using modified extended direct algebraic method

Cited by 8 publications

References 38 publications

Dynamics of optical solitons in the extended (3+1)‐dimensional nonlinear conformable Kudryashov equation with generalized anti‐cubic nonlinearity

Dynamics of optical solitons in the extended (3+1)‐dimensional nonlinear conformable Kudryashov equation with generalized anti‐cubic nonlinearity

Solitons, lump and interactional solutions of the (3+1)-dimensional BLMP equation in incompressible fluid

Propagation wave solutions with non-local nonlinearityfor stochastic NLSE

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