用新波变换研究（2+1）维克莱因-戈登方程中的非线性复波激励

IF 2.3 3区数学 Q1 MATHEMATICS

Mathematics Pub Date : 2024-09-14 DOI:10.3390/math12182867

Guojiang Wu, Yong Guo, Yanlin Yu

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引用次数: 0

摘要

克莱因--戈登方程在等离子体和凝聚态物理等数学物理中发挥着重要作用。探索其精确解有助于我们理解其复杂的非线性波现象。在本文中，我们首先提出了一种新的扩展雅各布椭圆函数展开方法，用于构建 (2+1)-dimensional Klein-Gordon 方程的丰富精确周期波解。然后，我们引入了一种新的波变换来构造非线性复波。为了证明这种方法的有效性，我们数值模拟了几组复波结构，这些结构显示了新型复波现象。结果表明，这种方法对于构建非线性方程的丰富精确解和复杂非线性波现象简单有效。

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

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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来源期刊

Mathematics Mathematics-General Mathematics

CiteScore

4.00

自引率

16.70%

发文量

4032

审稿时长

21.9 days

期刊介绍： Mathematics (ISSN 2227-7390) is an international, open access journal which provides an advanced forum for studies related to mathematical sciences. It devotes exclusively to the publication of high-quality reviews, regular research papers and short communications in all areas of pure and applied mathematics. Mathematics also publishes timely and thorough survey articles on current trends, new theoretical techniques, novel ideas and new mathematical tools in different branches of mathematics.