Shang Jiaxin, Li Wenhe, Li Da
School of Mathematics and Statistics, Northeast Petroleum University, 99 Xingzhi Street, Daqing, 163318, Heilongjiang Province, China.
Heliyon. 2023 Apr 25;9(5):e15695. doi: 10.1016/j.heliyon.2023.e15695. eCollection 2023 May.
The coupled Schrödinger-Korteweg-de Vries equation is a critical system of in nonlinear evolution equations. It describes various processes in dusty plasma, such as Langmuir waves, dust-acoustic waves, and electromagnetic waves. This paper uses the generalized coupled trial equation method to solve the equation. By the complete discrimination system for polynomial, a series of exact traveling wave solutions are obtained, including discontinuous periodic solutions, solitary wave solutions, and Jacobian elliptical function solutions. In addition, to determine the existence of the solutions and understand their properties, we draw three-dimensional images of the modules of the solutions with Mathematica. We obtain more comprehensive and accurate solutions than previous studies, and the results give the system more profound physical significance.
耦合的薛定谔-科特韦格-德弗里斯方程是一类重要的非线性演化方程组。它描述了尘埃等离子体中的各种过程，如朗缪尔波、尘埃声波和电磁波。本文采用广义耦合试方程法求解该方程。通过多项式的完全判别系统，得到了一系列精确的行波解，包括间断周期解、孤立波解和雅可比椭圆函数解。此外，为了确定解的存在性并了解其性质，我们用Mathematica绘制了解的模的三维图像。我们得到了比以往研究更全面、准确的解，这些结果赋予了该系统更深刻的物理意义。
