Solitons and other solutions to the nonlinear Bogoyavlenskii equations using the generalized Riccati equation mapping method

2017 ◽  
Vol 49 (11) ◽  
Author(s):  
Elsayed M. E. Zayed ◽  
Abdul-Ghani Al-Nowehy
Keyword(s):  
Riccati Equation ◽  
Mapping Method ◽  
Generalized Riccati Equation ◽  
Bogoyavlenskii Equations

Propagation of new dynamics of longitudinal bud equation among a magneto-electro-elastic round rod

2021 ◽  
Author(s):  
Mostafa M. A. Khater ◽  
Adil Jhangeer ◽  
Hadi Rezazadeh ◽  
Lanre Akinyemi ◽  
M. Ali Akbar ◽  
...  
Keyword(s):  
Differential Equations ◽  
Riccati Equation ◽  
Amorphous Silica ◽  
Plasma Frequency ◽  
Polarized Light ◽  
Metal Films ◽  
Mapping Method ◽  
Longitudinal Waves ◽  
Generalized Riccati Equation ◽  
Amorphous Substrates

In this survey, structure solutions for the longitudinal suspense equation within a magneto-electro-elastic (MEE) circular judgment are extracted via the implementation of two one-of-a-kind techniques that are viewed as the close generalized technique in its field. This paper describes the dynamics of the longitudinal suspense within a MEE round rod. Nilsson and Lindau provided the visual proof of the arrival concerning longitudinal waves within thin metal films. They recommended removal of anomalies between the ports concerning emaciated ([Formula: see text] Å) Ag layers preserved on amorphous silica because of being mildly [Formula: see text]-polarized at frequency tier according to the brawny plasma frequency. Anomalies have been due to confusion over the longitudinal waves mirrored utilizing the two borders. The wavelength is connected according to this wave’s property, which is an awful lot smaller than the wave over light. The wave is outstanding only for altogether superfine films. However, metallic movies defended amorphous substrates that are intermittent within the forward levels of their evolution. This made researchers aware of the possibility on getting ready altogether few layers with a desire to discussing the promulgation about longitudinal waves up to expectation colorful each among reverberation or transport on [Formula: see text]-polarized light. The mated options via the use of generalized Riccati equation mapping method or generalized Kudryashov technique show the rule and effectiveness regarding its methods then its ability because of applying one kind of forms over nonlinear incomplete differential equations.

Dynamic behaviors for a (2 + 1)-dimensional inhomogenous Heisenberg ferromagnetic spin chain system

2021 ◽  
pp. 2150251
Author(s):  
Douvagai ◽  
Yaouba Amadou ◽  
Gambo Betchewe ◽  
Alphonse Houwe ◽  
Mustafa Inc ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Riccati Equation ◽  
Spin Chain ◽  
Spin Dynamics ◽  
Semiclassical Limit ◽  
Mapping Method ◽  
Soliton Propagation ◽  
Generalized Riccati Equation ◽  
Heisenberg Ferromagnetic Spin Chain ◽  
Anisotropic Interactions

We investigate a (2 + 1)-dimensional nonlinear Schrodinger equation (NLSE), which describes the spin dynamics of (2 + 1)-dimensional inhomogeneous Heisenberg ferromagnetic spin chain (IHFSC) with bilinear and anisotropic interactions in the semiclassical limit. Miscellaneous new solitons solutions are obtained through the generalized Riccati equation mapping method (GREMM). Moreover, the effects of homogeneity on the soliton propagation and interaction are discussed. The derived structure of the obtain solutions offers a rich platform to better understand the nonlinear dynamics in the ferromagnetic materials.

scholarly journals Extended generalized Riccati equation mapping method for the fifth-order Sawada-Kotera equation

AIP Advances ◽  
2013 ◽  
Vol 3 (5) ◽  
pp. 052104 ◽  
Author(s):  
Hasibun Naher ◽  
Farah Aini Abdullah ◽  
Syed Tauseef Mohyud-Din
Keyword(s):  
Riccati Equation ◽  
Mapping Method ◽  
Generalized Riccati Equation ◽  
Fifth Order

scholarly journals Some new solutions of the conformable extended Zakharov-Kuznetsov equation using Atangana-Baleanu conformable derivative

2019 ◽  
Vol 23 (Suppl. 6) ◽  
pp. 2127-2137
Author(s):  
Bandar Bin-Mohsin
Keyword(s):  
Applied Sciences ◽  
Riccati Equation ◽  
Mapping Method ◽  
Conformable Derivative ◽  
Rational Solutions ◽  
Generalized Riccati Equation ◽  
Non Linear

The generalized Riccati equation mapping method, coupled with Atangana?s conformable derivative is implemented to solve non-linear extended Zakharov-Kuznetsov equation which results in producing hyperbolic, trigonometric and the rational solutions. The obtained results are new and are of great importance in engineering and applied sciences.

scholarly journals New Traveling Wave Solutions by the Extended Generalized Riccati Equation Mapping Method of the(2+1)-Dimensional Evolution Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Hasibun Naher ◽  
Farah Aini Abdullah
Keyword(s):  
Riccati Equation ◽  
Traveling Wave ◽  
Nonlinear Partial Differential Equations ◽  
Traveling Wave Solutions ◽  
Rational Functions ◽  
Mapping Method ◽  
Auxiliary Equation ◽  
Mathematical Tool ◽  
Wave Solutions ◽  
Generalized Riccati Equation

The generalized Riccati equation mapping is extended with the basic(G′/G)-expansion method which is powerful and straightforward mathematical tool for solving nonlinear partial differential equations. In this paper, we construct twenty-seven traveling wave solutions for the (2+1)-dimensional modified Zakharov-Kuznetsov equation by applying this method. Further, the auxiliary equationG′(η)=w+uG(η)+vG2(η)is executed with arbitrary constant coefficients and called the generalized Riccati equation. The obtained solutions including solitons and periodic solutions are illustrated through the hyperbolic functions, the trigonometric functions, and the rational functions. In addition, it is worth declaring that one of our solutions is identical for special case with already established result which verifies our other solutions. Moreover, some of obtained solutions are depicted in the figures with the aid of Maple.

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