非线性Broer-Kaup方程的相互作用解
The Interaction Solutions of the Non-Linear Broer-Kaup Equation
DOI: 10.12677/AAM.2020.97126, PDF,    科研立项经费支持
作者: 杨文欣, 陈怀堂：临沂大学数学与统计学院，山东 临沂
关键词: Broer-Kaup方程；相互作用解；辅助方程法；Broer-Kaup System； Interaction Solution； Auxiliary Equation Method
摘要: 随着人们对非线性方程的深入研究，经常通过探求非线性Broer-Kaup方程的相互作用解来描述水波等自然运动规律。本文提出了一种求非线性方程相互作用解的辅助方程新方法。该新方法可以很容易得到三角函数、指数函数、双曲函数和其他函数的混合函数解。利用该方法，我们成功地得到了(2 + 1)维Broer-Kaup方程的相互作用解。这些解在帮助物理学家准确分析相关领域中的特殊现象方面具有十分重要的理论意义和应用价值。
Abstract: With the deepening study of the non-linear equation, the interaction solutions of the non-linear Broer-Kaup equation are often used to describe the laws of natural motion such as water waves. In this paper, a new auxiliary equation method for obtaining the interaction solutions of nonlinear equations is proposed. The new method can easily obtain analytic multifunction solutions including trigonometric functions, exponential functions, hyperbolic functions and other functions. By using this method, we have successfully obtained the interaction solutions of the higher order (2 + 1) dimensional Broer-Kaup equation. It is significant to help physicists to analyze special phenomena in their relevant fields accurately.
文章引用：杨文欣, 陈怀堂. 非线性Broer-Kaup方程的相互作用解[J]. 应用数学进展, 2020, 9(7): 1066-1071. https://doi.org/10.12677/AAM.2020.97126

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