scholarly journals Interaction of electromagnetic wave and metamaterial with inductive type chiral inclusions

2021 ◽  
Vol 24 (2) ◽  
pp. 22-31
Author(s):  
Andrey N. Volobuev ◽  
Tatyana A. Antipova ◽  
Kaira A. Adyshirin-Zade
Keyword(s):  
Differential Equation ◽  
Electromagnetic Wave ◽  
Nonlinear Equation ◽  
Electromagnetic Radiation ◽  
Nonlinear Differential Equation ◽  
Standing Waves ◽  
Method Of Calculation ◽  
Inductive Type ◽  
Detailed Method

The principle of calculation of a plate from a metamaterial with inductive type chiral inclusions is submitted. It is shown that distribution of an electromagnetic wave to such substance can be investigated with the help of introduction of a chiral parameter and on the basis of a detailed method of calculation. By comparison of two methods the dependence of chiral parameter from frequency of electromagnetic radiation falling on a plate is found. With the help of a detailed method the nonlinear differential equation for potential on the chiral plate is found. It is shown that this equation has solutions as traveling solitary and standing waves but not traveling sine waves. The analysis of the received solutions of the nonlinear equation is carried out. Transition from the multiwave solution to the solution as standing waves is graphically shown at reduction ofdistance between the chiral elements.

scholarly journals Interaction of Electromagnetic Wave and Metamaterial with Inductive Type Chiral Inclusions

2020 ◽  
Vol 5 (3) ◽  
Author(s):  
A. N. Volobuev ◽  
Keyword(s):  
Differential Equation ◽  
Electromagnetic Wave ◽  
Nonlinear Equation ◽  
Electromagnetic Radiation ◽  
Nonlinear Differential Equation ◽  
Solitary Waves ◽  
Standing Waves ◽  
Method Of Calculation ◽  
Inductive Type ◽  
Detailed Method

The principle of calculation of a plate from a metamaterial with inductive type chiral inclusions is submitted. It is shown that distribution of an electromagnetic wave in such substance can be investigated with the help of using of a chiral parameter and on the basis of a detailed method of calculation. By comparison of two methods the dependence of chiral parameter from frequency of electromagnetic radiation falling on a plate is found. With the help of a detailed method the nonlinear differential equation for potential on the chiral plate is found. It is shown that this equation has solutions as traveling solitary waves and standing waves but not traveling sine waves. The analysis of the received solutions of the nonlinear equation is carried out. Transition from the multiwave solution to the solution as standing waves is graphically shown at reduction of distance between the chiral elements.

scholarly journals Parallel Solving Method for the Variable Coefficient Nonlinear Equation

2022 ◽  
Vol 16 ◽  
pp. 264-271
Author(s):  
Liling Shen
Keyword(s):  
Differential Equation ◽  
Nonlinear Equation ◽  
Linear Differential Equation ◽  
Nonlinear Differential Equation ◽  
Nonlinear Equations ◽  
Variable Coefficient ◽  
Expansion Method ◽  
Variable Coefficients ◽  
Traveling Wave Solution ◽  
Linear Differential

In view of the inaccuracy of traditional methods for solving nonlinear equations with variable coefficients in parallel, a new method for solving nonlinear equations with variable coefficients is proposed. Using the generalized symmetry group, the variable coefficient of the equation is taken as a new variable which is the same as the state of the original actual physical field. Some relations between variable coefficient equations and their solutions are found. This paper analyzes the meaning of linear differential equation and nonlinear differential equation, the difference between linear differential equation and nonlinear differential equation and their role in physics, and the necessity of solving nonlinear differential equation. By solving the nonlinear equation with variable coefficients, it can be seen that the general methods to solve the nonlinear equation include scattering inversion, Backlund transform and traveling wave solution. Based on the existing methods for solving nonlinear equations with variable coefficients, the homogeneous balance method is combined with the improved truncated expansion method, truncated expansion method and function reduction method, and the Hopf Cole transform and trial function are combined respectively. The above three methods are used to solve nonlinear equations with variable coefficients. Based on KdV Painleve principle, a parallel method for solving nonlinear equations with variable coefficients is proposed. Finally, it is proved that the method is accurate and effective for the parallel solution of nonlinear equations with variable coefficients.

Differential Transformation Method

2017 ◽  
pp. 140-172
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Nonlinear Equation ◽  
Nonlinear Differential Equation ◽  
Transformation Method ◽  
Differential Transformation Method ◽  
Differential Transformation

In this chapter, a new linearization procedure based on Differential Transformation Method (DTM) will be presented. The procedure begins with solving nonlinear differential equation by DTM. The effectiveness of the procedure is verified using a heat transfer nonlinear equation. The simulation result shows the significance of the proposed technique.

scholarly journals Closed form integration of the rotating plane pendulum nonlinear equation

2003 ◽  
Vol 34 (4) ◽  
pp. 327-350 ◽  
Author(s):  
Giovanni Mingari Scarpello ◽  
Daniele Ritelli
Keyword(s):  
Differential Equation ◽  
Nonlinear Equation ◽  
Closed Form ◽  
Nonlinear Differential Equation ◽  
Vertical Plane ◽  
Elliptic Functions ◽  
Angular Speed ◽  
Jacobi Elliptic Functions

The article deals with the nonlinear differential equation of the frictionless motion of a heavy pendulum swinging in a vertical plane which rotates at a fixed angular speed. The authors focused on its closed form integration by means of the Jacobi elliptic functions. This research took its origin by an autonomous work of the authors; this subject was also developed by [3], who did a treatment by far different from ours.

scholarly journals Oscillatory behavior of a second order nonlinear advanced differential equation with mixed neutral terms

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Hongwei Shi ◽  
Yuzhen Bai
Keyword(s):  
Differential Equation ◽  
Nonlinear Differential Equation ◽  
Oscillatory Behavior ◽  
Second Order ◽  
Oscillation Criteria ◽  
Order Nonlinear Differential Equation

AbstractIn this paper, we present several new oscillation criteria for a second order nonlinear differential equation with mixed neutral terms of the form $$ \bigl(r(t) \bigl(z'(t)\bigr)^{\alpha }\bigr)'+q(t)x^{\beta } \bigl(\sigma (t)\bigr)=0,\quad t\geq t_{0}, $$(r(t)(z′(t))α)′+q(t)xβ(σ(t))=0,t≥t0, where $z(t)=x(t)+p_{1}(t)x(\tau (t))+p_{2}(t)x(\lambda (t))$z(t)=x(t)+p1(t)x(τ(t))+p2(t)x(λ(t)) and α, β are ratios of two positive odd integers. Our results improve and complement some well-known results which were published recently in the literature. Two examples are given to illustrate the efficiency of our results.

scholarly journals Boundedness of Solutions to Differential Equations of Fourth Order with Oscillatory Restoring and Forcing Terms

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Cemil Tunç ◽  
Muzaffer Ateş
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Fourth Order ◽  
Cauchy Formula ◽  
Boundedness Of Solutions ◽  
Constant Coefficients ◽  
Particular Solution

This paper deals with the boundedness of solutions to a nonlinear differential equation of fourth order. Using the Cauchy formula for the particular solution of nonhomogeneous differential equations with constant coefficients, we prove that the solution and its derivatives up to order three are bounded.

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