Evolution equation for interaction of opposite directed waves with arbitrary polarization in 1D-metamaterial

2021 ◽  
Author(s):  
Dmitrii Ampilogov ◽  
Sergey Leble
Keyword(s):  
Traveling Wave ◽  
Electromagnetic Waves ◽  
Evolution Equations ◽  
Theoretical Study ◽  
Kerr Nonlinearity ◽  
Traveling Wave Solution ◽  
System Of Nonlinear Equations ◽  
Projection Operators ◽  
Polarized Waves ◽  
General Nonlinearity

In this paper, a theoretical study of wave propagation in 1D metamaterial is presented. A system of evolution equations for electromagnetic waves with both polarizations account is derived by means of projection operators method for general nonlinearity and dispersion. It describes interaction of opposite directed waves with a given polarization. The particular case of Kerr nonlinearity and Drude dispersion is considered. In such approximation, it results in the corresponding system of nonlinear equations that generalizes the Schäfer–Wayne one. Traveling wave solution for the system of equation of interaction of orthogonal-polarized waves is also obtained. Dependence of wavelength on amplitude is written and plotted.

scholarly journals Traveling-Wave Solution of Modified Liouville Equation by Means of Modified Simple Equation Method

2012 ◽  
Vol 2012 ◽  
pp. 1-4 ◽  
Author(s):  
Md. Abdus Salam
Keyword(s):  
Liouville Equation ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Traveling Wave Solutions ◽  
Traveling Wave Solution ◽  
Nonlinear Evolution Equations ◽  
Simple Equation ◽  
Equation Method ◽  
New Approach ◽  
Modified Simple Equation Method

We construct the traveling wave solutions involving parameters of modified Liouville equation by using a new approach, namely the modified simple equation method. The proposed method is direct, concise, and elementary and can be used for many other nonlinear evolution equations.

scholarly journals The solitary traveling wave solution for a class of nonlinear evolution equations

2014 ◽  
Vol 63 (13) ◽  
pp. 130201
Author(s):  
Shi Lan-Fang ◽  
Zhu Min ◽  
Zhou Xian-Chun ◽  
Wang Wei-Gang ◽  
Mo Jia-Qi
Keyword(s):  
Traveling Wave ◽  
Wave Solution ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solution ◽  
Nonlinear Evolution Equations

Traveling wave solutions for the Couple Boiti-Leon-Pempinelli System by using extended Jacobian elliptic function expansion method

2015 ◽  
Vol 11 (3) ◽  
pp. 3134-3138 ◽  
Author(s):  
Mostafa Khater ◽  
Mahmoud A.E. Abdelrahman
Keyword(s):  
Elliptic Function ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Nonlinear Evolution Equations ◽  
Jacobian Elliptic Function ◽  
Function Expansion

In this work, an extended Jacobian elliptic function expansion method is pro-posed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to the Couple Boiti-Leon-Pempinelli System which plays an important role in mathematical physics.

scholarly journals Single peaked traveling wave solutions to a generalized μ-Novikov Equation

2020 ◽  
Vol 10 (1) ◽  
pp. 66-75
Author(s):  
Byungsoo Moon
Keyword(s):  
Linear Combination ◽  
Traveling Wave ◽  
Wave Solution ◽  
Traveling Wave Solutions ◽  
Traveling Wave Solution ◽  
Wave Solutions ◽  
Quadratic Nonlinearities ◽  
Novikov Equation

Abstract In this paper, we study the existence of peaked traveling wave solution of the generalized μ-Novikov equation with nonlocal cubic and quadratic nonlinearities. The equation is a μ-version of a linear combination of the Novikov equation and Camassa-Hom equation. It is found that the equation admits single peaked traveling wave solutions.

Periodic traveling-wave solution of the Sakuma-Nishiguchi equation

1996 ◽  
Vol 54 (19) ◽  
pp. 13484-13486 ◽  
Author(s):  
David R. Rowland ◽  
Zlatko Jovanoski
Keyword(s):  
Traveling Wave ◽  
Wave Solution ◽  
Traveling Wave Solution ◽  
Periodic Traveling Wave

Explicit, periodic and dispersive soliton solutions to the conformable time-fractional Wu–Zhang system

2021 ◽  
pp. 2150417
Author(s):  
Kalim U. Tariq ◽  
Mostafa M. A. Khater ◽  
Muhammad Younis
Keyword(s):  
Fractional Derivative ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Nonlinear Evolution Equations ◽  
Conformable Fractional Derivative ◽  
Physical Behavior ◽  
Wave Solutions

In this paper, some new traveling wave solutions to the conformable time-fractional Wu–Zhang system are constructed with the help of the extended Fan sub-equation method. The conformable fractional derivative is employed to transform the fractional form of the system into ordinary differential system with an integer order. Some distinct types of figures are sketched to illustrate the physical behavior of the obtained solutions. The power and effective of the used method is shown and its ability for applying different forms of nonlinear evolution equations is also verified.

scholarly journals Synaptic propagation in neuronal networks with finite-support space dependent coupling

2020 ◽  
Author(s):  
Ricardo Erazo Toscano ◽  
Remus Osan
Keyword(s):  
Time Constant ◽  
Sensory Processing ◽  
Traveling Waves ◽  
Traveling Wave ◽  
Neuronal Networks ◽  
Evolution Equations ◽  
Network Connectivity ◽  
Space Constant ◽  
The Stability ◽  
The Brain

1AbstractTraveling waves of electrical activity are ubiquitous in biological neuronal networks. Traveling waves in the brain are associated with sensory processing, phase coding, and sleep. The neuron and network parameters that determine traveling waves’ evolution are synaptic space constant, synaptic conductance, membrane time constant, and synaptic decay time constant. We used an abstract neuron model to investigate the propagation characteristics of traveling wave activity. We formulated a set of evolution equations based on the network connectivity parameters. We numerically investigated the stability of the traveling wave propagation with a series of perturbations with biological relevance.

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