scholarly journals Soliton Solutions for space-time fractional Heisenberg ferromagnetic spin chain equation by generalized Kudryashov method and modified exp -expansion function method

2021 ◽  
Vol 67 (3 May-Jun) ◽  
pp. 393
Author(s):  
S. Tuluce Demiray ◽  
U. Bayrakci
Keyword(s):  
Spin Chain ◽  
Function Method ◽  
Time Derivative ◽  
Soliton Solutions ◽  
Bright Soliton ◽  
Integration Schemes ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method ◽  
Heisenberg Ferromagnetic Spin Chain ◽  
Chain Equation

This paper addresses the Heisenberg ferromagnetic spin chain equation with beta time derivative. Integration schemes are used to study this equation. They are generalized Kudryashov method and modified exp -expansion function method. Dark, bright and dark-bright soliton solutions of this equation are procured.

SOLITONS AND OTHER SOLUTIONS FOR THE (2+1)-DIMENSIONAL HEISENBERG FERROMAGNETIC SPIN CHAIN EQUATION USING IMPROVED MODIFIED EXTENDED TANH-FUNCTION METHOD

2021 ◽  
Vol 10 (11) ◽  
pp. 3491-3504
Author(s):  
A. Darwish ◽  
H.M. Ahmed ◽  
M. Ammar ◽  
M.H. Ali ◽  
A.H. Arnous
Keyword(s):  
Periodic Solutions ◽  
Exponential Function ◽  
Spin Chain ◽  
Function Method ◽  
Chain Model ◽  
Bright Solitons ◽  
Dark Solitons ◽  
Heisenberg Ferromagnetic Spin Chain ◽  
Spin Chain Model ◽  
Chain Equation

This paper studies $(2 + 1)$-dimensional Heisenberg ferromagnetic spin chain model by using improved modified extended tanh-function method. Various types of solutions are extracted such as bright solitons, singular solitons, dark solitons, singular periodic solutions, Weierstrass elliptic periodic type solutions and exponential function solutions. Moreover, some of the obtained solutions are represented graphically.

scholarly journals Investigation of Dark and Bright Soliton Solutions of Some Nonlinear Evolution Equations

2018 ◽  
Vol 22 ◽  
pp. 01056 ◽  
Author(s):  
Seyma Tuluce Demiray ◽  
Hasan Bulut
Keyword(s):  
Exact Solutions ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Nonlinear Evolution Equations ◽  
Bright Soliton ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method ◽  
Ostrovsky Equation

In this paper, generalized Kudryashov method (GKM) is used to find the exact solutions of (1+1) dimensional nonlinear Ostrovsky equation and (4+1) dimensional Fokas equation. Firstly, we get dark and bright soliton solutions of these equations using GKM. Then, we remark the results we found using this method.

Investigation of various soliton solutions to the Heisenberg ferromagnetic spin chain equation

2017 ◽  
Vol 32 (9) ◽  
pp. 1093-1105 ◽  
Author(s):  
Tukur Abdulkadir Sulaiman ◽  
Tolga Aktürk ◽  
Hasan Bulut ◽  
Haci Mehmet Baskonus
Keyword(s):  
Spin Chain ◽  
Soliton Solutions ◽  
Heisenberg Ferromagnetic Spin Chain ◽  
Chain Equation

scholarly journals New soliton solutions of the system of equations for the ion sound and Langmuir waves

2016 ◽  
Vol 7 (1) ◽  
pp. 42-49
Author(s):  
Seyma Tuluce Demiray ◽  
Hasan Bulut
Keyword(s):  
Sound Wave ◽  
High Frequency ◽  
Ponderomotive Force ◽  
Soliton Solutions ◽  
Langmuir Wave ◽  
Dark Soliton ◽  
System Of Equations ◽  
Langmuir Waves ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method

This study is based on new soliton solutions of the system of equations for the ion sound wave under the action of the ponderomotive force due to high-frequency field and for the Langmuir wave. The generalized Kudryashov method (GKM), which is one of the analytical methods, has been tackled for finding exact solutions of the system of equations for the ion sound wave and the Langmuir wave. By using this method, dark soliton solutions of this system of equations have been obtained. Also, by using Mathematica Release 9, some graphical simulations were designed to see the behavior of these solutions.

Dark solitons, Lax pair and infinitely-many conservation laws for a generalized (2+1)-dimensional variable-coefficient nonlinear Schrödinger equation in the inhomogeneous Heisenberg ferromagnetic spin chain

2017 ◽  
Vol 31 (03) ◽  
pp. 1750013 ◽  
Author(s):  
Xue-Hui Zhao ◽  
Bo Tian ◽  
De-Yin Liu ◽  
Xiao-Yu Wu ◽  
Jun Chai ◽  
...  
Keyword(s):  
Conservation Laws ◽  
Spin Chain ◽  
Variable Coefficient ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Lax Pair ◽  
Nonlinear Schrodinger Equation ◽  
Dark Solitons ◽  
Heisenberg Ferromagnetic Spin Chain ◽  
Dimensional Variable

Under investigation in this paper is a generalized (2+1)-dimensional variable-coefficient nonlinear Schrödinger equation in an inhomogeneous Heisenberg ferromagnetic spin chain. Lax pair and infinitely-many conservation laws are derived, indicating the existence of the multi-soliton solutions for such an equation. Via the Hirota method with an auxiliary function, bilinear forms, dark one-, two- and three-soliton solutions are derived. Propagation and interactions for the dark solitons are illustrated graphically: Velocity of the solitons is linearly related to the coefficients of the second- and fourth-order dispersion terms, while amplitude of the solitons does not depend on them. Interactions between the two solitons are shown to be elastic, while those among the three solitons are pairwise elastic.

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