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.

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.

New traveling wave solutions of the perturbed nonlinear Schrödingers equation in the left-handed metamaterials

2018 ◽  
Vol 13 (01) ◽  
pp. 2050022 ◽  
Author(s):  
Alphonse Houwe ◽  
Mibaile Justin ◽  
Serge Y. Doka ◽  
Kofane Timoleon Crepin
Keyword(s):  
Exact Solutions ◽  
Traveling Wave ◽  
Fiber Optic ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Simple Equation ◽  
Left Handed ◽  
Wave Solutions ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method

This paper extracts the analytical soliton solutions of the perturbed NLSE given in (1). We use successfully two integration methods namely the extended simple equation method and generalized Kudryashov method. In view of the results obtained, some new additional ones have been obtained. The results are dark, bright and exact solutions that propagate in the fiber optic and left-handed metamaterials (LHMs).

scholarly journals Novel soliton solutions to the Atangana–Baleanu fractional system of equations for the ISALWs

Open Physics ◽  
2021 ◽  
Vol 19 (1) ◽  
pp. 770-779
Author(s):  
Muhammad Imran Asjad ◽  
Naeem Ullah ◽  
Hamood Ur Rehman ◽  
Tuan Nguyen Gia
Keyword(s):  
Soliton Solutions ◽  
System Of Equations ◽  
Langmuir Waves ◽  
Bright Solitons ◽  
Dark Solitons ◽  
Direct Technique ◽  
Fractional Models ◽  
Fractional System ◽  
Background Wave ◽  
Physical Phenomena

Abstract This work deals the construction of novel soliton solutions to the Atangana–Baleanu (AB) fractional system of equations for the ion sound and Langmuir waves by using Sardar-subequation method (SSM). The outcomes are in the form of bright, singular, dark and combo soliton solutions. These solutions have wide applications in the arena of optoelectronics and wave propagation. The bright solitons will be a vast advantage in controlling the soliton disorder, dark solitons are also beneficial for soliton communication when a background wave exists and singular solitons only elaborate the shape of solitons and show a total spectrum of soliton solutions created from the model. These results would be very helpful to study and understand the physical phenomena in nonlinear optics. The performance of the SSM shows that this is powerful, talented, suitable and direct technique to discover the exact solutions for a number of nonlinear fractional models.

Rogue waves generation and interaction of multipeak rational solitons in the system of equations for the ion sound and Langmuir waves

2019 ◽  
Vol 33 (24) ◽  
pp. 1950277 ◽  
Author(s):  
Iftikhar Ahmed ◽  
Aly R. Seadawy ◽  
Dianchen Lu
Keyword(s):  
Rogue Wave ◽  
Soliton Solutions ◽  
Quadratic Function ◽  
Rogue Waves ◽  
System Of Equations ◽  
3D Graphics ◽  
Langmuir Waves ◽  
Double Exponential ◽  
Different Types ◽  
Multiwave Solutions

In this paper, our purpose is to construct multiwave solutions for the system of equations for the ion sound and Langmuir waves (SEISLWs) by utilizing the traveling wave and logarithmic transformation with the help of symbolic computation and the ansatz function method. We apply three distinctive approaches: namely, positive quadratic function approach, three waves approach and double exponential approach. By choosing suitable parametric values, 3D graphics are plotted to get different types of multiwave solutions including lump waves, rogue wave and multipeak soliton solutions. Moreover, we revealed very interesting multiwaves interactional phenomena.

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.

scholarly journals Photon polarizability and its effect on the dispersion of plasma waves

2017 ◽  
Vol 83 (2) ◽  
Author(s):  
I. Y. Dodin ◽  
D. E. Ruiz
Keyword(s):  
High Frequency ◽  
Ponderomotive Force ◽  
Plasma Waves ◽  
Detailed Calculation ◽  
Governing Equations ◽  
Langmuir Waves ◽  
Electron Fluid ◽  
Ponderomotive Forces ◽  
Linear Plasma

High-frequency photons travelling in plasma exhibit a linear polarizability that can influence the dispersion of linear plasma waves. We present a detailed calculation of this effect for Langmuir waves as a characteristic example. Two alternative formulations are given. In the first formulation, we calculate the modified dispersion of Langmuir waves by solving the governing equations for the electron fluid, where the photon contribution enters as a ponderomotive force. In the second formulation, we provide a derivation based on the photon polarizability. Then, the calculation of ponderomotive forces is not needed, and the result is more general.

scholarly journals Soliton solutions of nonlinear fractional differential equations with its applications in mathematical physics

2021 ◽  
Vol 67 (3 May-Jun) ◽  
pp. 422
Author(s):  
A. C. Çevikel ◽  
E. Aksoy
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Soliton Solutions ◽  
Mathematical Physics ◽  
Nonlinear Fractional Differential Equations ◽  
Fractional Complex Transform ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method ◽  
Present Technique ◽  
Fractional Differential

Generalized Kudryashov method has been used to private type of nonlinear fractional differential equations. Firstly, we proposed a fractional complex transform to convert fractional differential equations into ordinary differential equations. Three applications were given to demonstrate the effectiveness of the present technique. As a result, abundant types of exact analytical solutions are obtained.

New Jacobi elliptic solutions and other solutions with quadratic-cubic nonlinearity using two mathematical methods

2018 ◽  
Vol 13 (02) ◽  
pp. 2050043 ◽  
Author(s):  
Savaissou Nestor ◽  
Mibaile Justin ◽  
Douvagai ◽  
Gambo Betchewe ◽  
Serge Y. Doka ◽  
...  
Keyword(s):  
Exact Solutions ◽  
Soliton Solutions ◽  
Higher Order ◽  
Auxiliary Equation ◽  
Cubic Nonlinearity ◽  
Mathematical Methods ◽  
Auxiliary Equation Method ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method ◽  
Elliptic Solutions

In this paper, we apply two powerful methods, namely, the new extended auxiliary equation method and the generalized Kudryashov method for constructing many exact solutions and other solutions for the higher order dispersive nonlinear Schrödinger’s equation to secure soliton solutions in quadratic-cubic medium. Various solutions of the resulting nonlinear ODE are obtained by using the above two methods.

Transition between Raman and Compton regimes in laser pulse amplification

2010 ◽  
Vol 76 (3-4) ◽  
pp. 395-401 ◽  
Author(s):  
R. A. CAIRNS
Keyword(s):  
Simple Model ◽  
Laser Pulse ◽  
High Frequency ◽  
Ponderomotive Force ◽  
Langmuir Wave ◽  
Electron Dynamics ◽  
Single Particles ◽  
Frequency Wave ◽  
Pulse Amplification ◽  
Long Pulse

AbstractAmplification of a short laser pulse by means of its interaction with a counter-propagating long pulse in a plasma has been suggested as a way of reaching high intensities. Two regimes have been discussed in the literature. The first is the Raman regime, where the process is backward Raman scattering, described by the standard equations for resonant three-wave coupling, while the second is the Compton regime, in which electron dynamics is dominated by the ponderomotive force generated by the high-frequency wave, and electrons behave as single particles rather than producing a Langmuir wave. Our aim here is to use a simple model of electron dynamics to investigate the transition between these regimes.

Sign in / Sign up

Export Citation Format

Share Document