Hirota-Satsuma耦合KdV方程组的行波解  

Traveling Wave Solutions of Hirota-Satsuma Coupled KdV Equation

作　　者：李文赫 尚佳鑫 LI WENHE;SHANG JIAXIN(School of Mathematics and Statistics,Northeast Petroleum University,Daqing 163318,China)

机构地区：[1]东北石油大学数学与统计学院,大庆163318

出　　处：《应用数学学报》2022年第4期500-508,共9页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金数学天元基金(No.12126312);黑龙江省省属本科高校基本科研业务费特色科研团队专项(No.2022TSTD-05)资助项目.

摘　　要：非线性发展方程在工程技术领域有广泛的应用,求非线性微分方程的精确解一直是其中的重点和难点目前已经提出了许多求解方法,如反散射方法、李群方法、Backlund变换方法及一些直接展开方法,包括双线性方法、混合指数法、齐次平衡法、双曲函数展开法、Jacobi椭圆函数展开法等本文在试探方程法的基础上提出了耦合试探方程法,求解了一个描述具有不同色散关系的两个长波相互作用的Hirota Satsuma耦合KdV方程组,再借助多项式完全判别系统给出了该方程组行波解的分类,得到了四组孤立波解,两组不连续周期解和七组Jacobi椭圆函数解.通过与其他文献的比较,我们得到的解包括其中的一些解,并且得到了用其他方法目前尚未得到的新解.Nonlinear evolution equations are widely used in the field of engineering technology.To get the exact solution by solving nonlinear differential equations is always the focus and difficulty.At present,many methods for solving equations have been proposed,such as scatter inversion method,Lie group method,Backhmd transformation method and some direct expansion methods,including bilinear method,mixed exponential method,homogeneous equilibrium method,hyperbolic function expansion method,Jacobi elliptic function expansion method and so on.In this paper,we proposed a coupled trial equations method based on the trial equation method.The Hirota-Satsuma coupled KdV equations describing the interaction of two long waves with different dispersion relations are solved by it.Then the classifications of traveling wave solutions of the equations are given by the complete discrimination system for polynomial,including four groups of solitary wave solutions,two groups of discontinuous periodic solutions and seven groups of Jacobi elliptic function solutions are obtained.Compared with the solutions obtained in other literatures,our solutions not only include them,but also include new solutions,which have not been obtained by other methods.

关 键 词：Hirota-Satsuma耦合KdV方程组 试探方程法 多项式完全判别系统 行波解 

分 类 号：O211.61[理学—概率论与数理统计]