scholarly journals Soliton solutions for non-linear Kudryashov's equation via three integrating schemes

2021 ◽  
Vol 25 (Spec. issue 2) ◽  
pp. 157-163
Author(s):  
Saima Arshed ◽  
Mehdi Mirhosseini-Alizamini ◽  
Dumitru Baleanu ◽  
Hadi Rezazadeh ◽  
Mustafa Inc ◽  
...  
Keyword(s):  
Refractive Index ◽  
State Of The Art ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Auxiliary Equation ◽  
Art Integration ◽  
Auxiliary Equation Method ◽  
Integration Schemes ◽  
Proposed Model ◽  
Non Linear

This paper considers the non-linear Kudryashov's equation, that is an extension of the well-known dual-power law of refractive index and is analog to the generalized version of anti-cubic non-linearity. The model is considered in the presence of full non-linearity. The main objective of this paper is to extract soliton solutions of the proposed model. Three state-of-the-art integration schemes, namely modified auxiliary equation method, the sine-Gordon expansion method and the tanhcoth expansion method have been employed for obtaining the desired soliton solutions.

scholarly journals Optical Solutions in Fiber Bragg Gratings with Polynomial Law Nonlinearity and Cubic-Quartic Dispersive Reflectivity-=SUP=-*-=/SUP=-

2021 ◽  
Vol 129 (11) ◽  
pp. 1409
Author(s):  
Elsayed M.E. Zayed ◽  
Mohamed E.M. Alngar ◽  
Anjan Biswas ◽  
Mehmet Ekici ◽  
Padmaja Guggilla ◽  
...  
Keyword(s):  
Refractive Index ◽  
Periodic Solutions ◽  
Nonlinear Refractive Index ◽  
Fiber Bragg Gratings ◽  
Soliton Solutions ◽  
Bragg Gratings ◽  
Optical Solitons ◽  
Auxiliary Equation ◽  
Equation Approach ◽  
Integration Schemes

Optical solitons with ber Bragg gratings and polynomial law of nonlinear refractive index are addressed in the paper. The auxiliary equation approach together with an addendum to Kudryashov's method identify soliton solutions to the model. Singular periodic solutions emerge from these integration schemes as a byproduct. Keywords: solitons; cubic-quartic; Bragg gratings.

scholarly journals New and More Solitary Wave Solutions for the Klein-Gordon-Schrödinger Model Arising in Nucleon-Meson Interaction

2021 ◽  
Vol 9 ◽  
Author(s):  
Nauman Raza ◽  
Saima Arshed ◽  
Asma Rashid Butt ◽  
Dumitru Baleanu
Keyword(s):  
Soliton Solutions ◽  
Expansion Method ◽  
Dark Soliton ◽  
Art Integration ◽  
Scalar Mesons ◽  
Integration Schemes ◽  
Klein Gordon ◽  
Physical Features ◽  
Existence Criteria ◽  
Singular Soliton

This paper considers methods to extract exact, explicit, and new single soliton solutions related to the nonlinear Klein-Gordon-Schrödinger model that is utilized in the study of neutral scalar mesons associated with conserved scalar nucleons coupled through the Yukawa interaction. Three state of the art integration schemes, namely, the e−Φ(ξ)-expansion method, Kudryashov's method, and the tanh-coth expansion method are employed to extract bright soliton, dark soliton, periodic soliton, combo soliton, kink soliton, and singular soliton solutions. All the constructed solutions satisfy their existence criteria. It is shown that these methods are concise, straightforward, promising, and reliable mathematical tools to untangle the physical features of mathematical physics equations.

New and more fractional soliton solutions related to generalized Davey–Stewartson equation using oblique wave transformation

2021 ◽  
pp. 2150317
Author(s):  
Nauman Raza ◽  
Saima Arshed ◽  
Kashif Ali Khan ◽  
Dumitru Baleanu
Keyword(s):  
Soliton Solutions ◽  
Finite Depth ◽  
Wave Transformation ◽  
Auxiliary Equation ◽  
Oblique Wave ◽  
Integration Schemes ◽  
Proposed Model ◽  
Dominant Feature ◽  
Temporal Derivative ◽  
Propagation Of Waves

The generalized fractional Davey–Stewartson (DSS) equation with fractional temporal derivative, which is used to explore the trends of wave propagation in water of finite depth under the effects of gravity force and surface tension, is considered in this paper. The paper addresses the full nonlinearity of the proposed model. To extract the oblique soliton solutions of the generalized fractional DSS (FDSS) equation is the dominant feature of this research. The conformable fractional derivative is used for fractional temporal derivative and oblique wave transformation is used for converting the proposed model into ordinary differential equation. Two state-of-the-art integration schemes, modified auxiliary equation (MAE) and generalized projective Riccati equations (GPREs) method have been employed for obtaining the desired oblique soliton solutions. The proposed methods successfully attain different structures of explicit solutions such as bright, dark, singular, and periodic solitary wave solutions. The occurrence of these results ensured by the limitations utilized is also exceptionally promising to additionally investigate the propagation of waves of finite depth. The latest found solutions with their existence criteria are considered. The 2D and 3D portraits are also shown for some of the reported solutions. From the graphical representations, it have been illustrated that the descriptions of waves are changed along with the change in fractional and obliqueness parameters.

scholarly journals Stability and Extraction of New Optical Wave Solutions of Cascaded System in (2 + 1)-dimensions

2021 ◽  
Author(s):  
Hitender Kumar ◽  
Parveen Parveen ◽  
Sunita Dahiya ◽  
Anand Kumar ◽  
Manjeet Singh Gautam
Keyword(s):  
Elliptic Function ◽  
Data Transfer ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Dynamical Behaviour ◽  
Auxiliary Equation ◽  
Jacobi Elliptic Function ◽  
Optical Wave ◽  
Auxiliary Equation Method ◽  
Weierstrass Elliptic Function

Abstract This paper uses the new modified sub-ODE method, the new extended auxiliary equation method, and the new Jacobi elliptic function expansion method to revisit the (2+1)-dimensional coupled nonlinear Schr¨odinger equation with cascading effect. As a consequence, dark, bright, kinkantikink, singular solitons, Weierstrass elliptic function, doubly periodic, and complex optical soliton solutions are retrieved. All solutions are described, along with the existence criterion on the parameters. As solitons are used for data transfer, the obtained results may be found usage in optical couplers, birefringed fibres, and optoelectronic devices. A comparison of the obtained results with those found in the literature is given. The dynamical behaviour of some of the obtained solutions has been explored for suitable choices of the parameters. Using the property of Hamiltonian systems, the solitons stability is determined.

scholarly journals Cubic-Quartic Optical Solitons in Bragg Gratings Fibers for Perturbed NLSE Having Parabolic-Nonlocal Law of Refractive Index Using Two Integration Schemes

2021 ◽  
Author(s):  
Elsayed M. E. Zayed ◽  
Mohamed E. M. Alngar
Keyword(s):  
Refractive Index ◽  
Bragg Gratings ◽  
Optical Solitons ◽  
Equation Method ◽  
Auxiliary Equation ◽  
Auxiliary Equation Method ◽  
Integration Schemes ◽  
Existence Criteria

Abstract The optical solitons in Bragg gratings fibers for perturbed NLSE having cubic-quartic dispersive reflectivity with parabolic-nonlocal combo law of refractive index are studied. The extended auxiliary equation method and the addendum to Kudryashov's method are introduced. The existence criteria for such solitons are indicated.

Simulation of bright–dark soliton solutions of the Lonngren wave equation arising the model of transmission lines

2021 ◽  
pp. 2150484
Author(s):  
Asif Yokuş
Keyword(s):  
Wave Equation ◽  
Soliton Solutions ◽  
Stationary Wave ◽  
Dark Soliton ◽  
Traveling Wave Solution ◽  
Bright Soliton ◽  
Auxiliary Equation ◽  
Discussion Section ◽  
Auxiliary Equation Method ◽  
Advantages And Disadvantages

In this study, the auxiliary equation method is applied successfully to the Lonngren wave equation. Bright soliton, bright–dark soliton solutions are produced, which play an important role in the distribution and distribution of electric charge. In the conclusion and discussion section, the effect of nonlinearity term on wave behavior in bright soliton traveling wave solution is examined. The advantages and disadvantages of the method are discussed. While graphs representing the stationary wave are obtained, special values are given to the constants in the solutions. These graphs are presented as 3D, 2D and contour.

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