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Open AccessArticle
Nonlinear Complex Wave Excitations in (2+1)-Dimensional Klein–Gordon Equation Investigated by New Wave Transformation
by
Guojiang Wu
Guojiang Wu 1,
Yong Guo
Yong Guo 2,* and
Yanlin Yu
Yanlin Yu 1,*
1
School of Science, Kaili University, Kaili 556000, China
2
Institute of Plasma Physics, Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei 230031, China
*
Authors to whom correspondence should be addressed.
Mathematics 2024, 12(18), 2867; https://doi.org/10.3390/math12182867 (registering DOI)
Submission received: 14 August 2024
/
Revised: 9 September 2024
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Accepted: 13 September 2024
/
Published: 14 September 2024
Abstract
The Klein–-Gordon equation plays an important role in mathematical physics, such as plasma and, condensed matter physics. Exploring its exact solution helps us understand its complex nonlinear wave phenomena. In this paper, we first propose a new extended Jacobian elliptic function expansion method for constructing rich exact periodic wave solutions of the (2+1)-dimensional Klein–-Gordon equation. Then, we introduce a novel wave transformation for constructing nonlinear complex waves. To demonstrate the effectiveness of this method, we numerically simulated several sets of complex wave structures, which indicate new types of complex wave phenomena. The results show that this method is simple and effective for constructing rich exact solutions and complex nonlinear wave phenomena to nonlinear equations.
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MDPI and ACS Style
Wu, G.; Guo, Y.; Yu, Y.
Nonlinear Complex Wave Excitations in (2+1)-Dimensional Klein–Gordon Equation Investigated by New Wave Transformation. Mathematics 2024, 12, 2867.
https://doi.org/10.3390/math12182867
AMA Style
Wu G, Guo Y, Yu Y.
Nonlinear Complex Wave Excitations in (2+1)-Dimensional Klein–Gordon Equation Investigated by New Wave Transformation. Mathematics. 2024; 12(18):2867.
https://doi.org/10.3390/math12182867
Chicago/Turabian Style
Wu, Guojiang, Yong Guo, and Yanlin Yu.
2024. "Nonlinear Complex Wave Excitations in (2+1)-Dimensional Klein–Gordon Equation Investigated by New Wave Transformation" Mathematics 12, no. 18: 2867.
https://doi.org/10.3390/math12182867
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