Nonlinear Complex Wave Excitations in (2+1)-Dimensional Klein–Gordon Equation Investigated by New Wave Transformation

Guojiang Wu, Yong Guo () and Yanlin Yu ()
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Guojiang Wu: School of Science, Kaili University, Kaili 556000, China
Yong Guo: Institute of Plasma Physics, Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei 230031, China
Yanlin Yu: School of Science, Kaili University, Kaili 556000, China

Mathematics, 2024, vol. 12, issue 18, 1-17

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.

Keywords: (2+1)-dimensional Klein–Gordon equation; Jacobian elliptic function; auxiliary equation; nonlinear evolution equation; complex wave structure (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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