A new approach for modelling the damped Helmholtz oscillator:applications to plasma physics and electronic circuits

作     者：S A El-Tantawy Alvaro H Salas M R Alharthi S A El-Tantawy;Alvaro H Salas;M R Alharthi

作者机构：Department of PhysicsFaculty of SciencePort Said UniversityPort Said 42521Egypt Research Center for Physics(RCP)Department of PhysicsFaculty of Science and ArtsAl-MikhwahAl-Baha UniversitySaudi Arabia Department of MathematicsUniversidad National de ColombiaUniversidad National de Colombia-Nubia Campus Derpartment of Mathematics and Statistics FIZMAKO Research GroupColombia Department of Mathematics and StatisticsCollege of ScienceTaif UniversityPO Box 11099Taif 21944Saudi Arabia 

出 版 物：《Communications in Theoretical Physics》 (理论物理通讯（英文版）)

年 卷 期：2021年第73卷第3期

页      面：119-130页

核心收录：

学科分类：080904[工学-电磁场与微波技术] 0809[工学-电子科学与技术（可授工学、理学学位）] 07[理学] 08[工学] 070204[理学-等离子体物理] 0704[理学-天文学] 0702[理学-物理学] 

基　　金：Taif University Researchers Supporting Project number(TURSP-2020/275) Taif University Taif Saudi Arabia 

主　　题：damped and undamped Helmholtz equation Korteweg-de Vries type equation plasma oscillations nonlinear RLC circuits Weierstrass ellliptic function periodical solution 

摘      要：In this paper,a new approach is devoted to find novel analytical and approximate solutions to the damped quadratic nonlinear Helmholtz equation(HE)in terms of the Weiersrtrass elliptic *** exact solution for undamped HE(integrable case)and approximate/semi-analytical solution to the damped HE(non-integrable case)are given for any arbitrary initial *** a special case,the necessary and sufficient condition for the integrability of the damped HE using an elementary approach is *** general,a new ansatz is suggested to find a semi-analytical solution to the non-integrable case in the form of Weierstrass elliptic *** addition,the relation between the Weierstrass and Jacobian elliptic functions solutions to the integrable case will be derived in ***,we will make a comparison between the semi-analytical solution and the approximate numerical solutions via using Runge-Kutta fourth-order method,finite difference method,and homotopy perturbation method for the first-two ***,the maximum distance errors between the approximate/semi-analytical solution and the approximate numerical solutions will be *** real applications,the obtained solutions will be devoted to describe the characteristics behavior of the oscillations in RLC series circuits and in various plasma models such as electronegative complex plasma model.