Semi-inverse Method to the Klein-Gordon Equation with Quadratic Nonlinearity
Keywords:
Dynamics equation, electromagnetic transmission, nonlinear equation, semi-inverse method, solitary solutionAbstract
Nonlinear electrical and mechanical systems have been widely used in the industry electronics and consumer devices. Many numerical algorithms can be employed to obtain the numerical solutions of the nonlinear dynamics or electromagnetic equations. However, it takes a lot of time and decreases the solution accuracy. In this paper, a novel method, called Semi- Inverse Method, is proposed to seek solitary solutions of nonlinear differential equations. The Klein-Gordon equation with quadratic nonlinearity is selected to illustrate the effectiveness and simplicity of the suggested method.
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References
D. M. Diego and R. Adroaldo, “Electromagnetic modeling of electronic device by electrical circuit parameters,” Applied Computational Electromagnetics Society Journal, vol. 31, pp. 58-65, 2016.
M. Naser-Moghadasi, “Harmonic suppression of parallel coupled-line bandpass filters using defected microstrip structure,” Applied Computational Electromagnetics Society Journal, vol. 31, pp. 568-573, 2016.
W. Yan, Q. Tang, and E. Wang, “Radiated emission mechanism for semi-active control strategy of magneto-rheological damper,”International Journal of Applied Electromagnetics and Mechanics, vol. 51, pp. 185-198, 2016.
W. Yan, J. Yu, and Q. Tang, “Analysis and mitigation on conducted electromagnetic interference of semi-active control strategy for magnetorheological damper,” International Journal of Applied Electromagnetics and Mechanics, vol. 50, pp. 247-254, 2016.
I. Mahmoud, M. Fathallah, and H. Rehaoulia, “Nonlinear modelling approach for linear switched reluctance motor and its validation by two dimensional FEA,” Applied Computational Electromagnetics Society Journal, vol. 31, pp. 195-203, 2016.
R. G. Ilinger and D. B. Davidson, “The computational performance and power consumption of the parallel FDTD on a smartphone platform,” Applied Computational Electromagnetics Society Journal, vol. 30, pp. 1262-1268, 2015.
R. K. Murphy, H. A. Sabbagh, and E. H. Sabbagh, “A multiscale algorithm for eddy-current nondestructive evaluation based on volume-integral equations: Initial concepts,” Applied Computational Electromagnetics Society Journal, vol. 31, pp. 333-339, 2016.
H. Xu, D. Z. Ding, and R. S. Chen, “A hybrid explicit-implicit scheme for spectral-element timedomain analysis of multiscale simulation,” Applied Computational Electromagnetics Society Journal, vol. 31, pp. 444-449, 2016.
L. E. Sun and W. C. Chew, “Modeling of anisotropic magnetic objects by volume integral equation methods,”Applied Computational Electromagnetics Society Journal, vol. 30, pp. 1256-1261, 2015.
J.-H. He and L.-N. Zhang, “Generalized solitary solution and compacton-like solution of the JaulentMiodek equations using the Exp-function method,” Physics Letters A, vol. 372, pp. 1044-1047, 2008.
F. Xu and W. Yan, “Evaluation of two-dimensional ZK-MEW equation using the Exp-function method,” Computers & Mathematics with Applications, vol. 58, pp. 2307-2312, 2009.
A. M. Wazwaz, “The extended tanh method for the Zakharov-Kuznetsov (ZK) equation, the modified ZK equation, and its generalized forms,” Communications in Nonlinear Science and Numerical Simulation, vol. 13, pp. 1039-1047, 2008.
H. Zhao, “Applications of the generalized algebraic method to special-type nonlinear equations,” Chaos, Solitons & Fractals, vol. 36, pp. 359-369, 2008.
C. H. Schmidt and T. F. Eibert, “Integral equation methods for near-field far-field transformation,” Applied Computational Electromagnetics Society Journal, vol. 25, pp. 15-22, 2010.
Y. Xu, H. Yang, and W. Yu, “Scattering analysis of periodic composite metallic and dielectric structures with synthetic basis functions,” Applied Computational Electromagnetics Society Journal, vol. 30, pp. 1059-1067, 2015.
M. F. Xue and J. M. Jin, “Finite-element domain decomposition methods for analysis of large-scale electromagnetic problems,” Applied Computational Electromagnetics Society Journal, vol. 29, pp. 990-1002, 2014.
