摘要
为了寻求含色散长波方程组精确解的合适方法,利用范恩贵在《可积系统与计算机代数》一书中提出的这种基于符号计算的一种代数方法统一构造非线性方程的孤子解、有理解、和周期解。在对方程组作行波变换的基础上,假设方程具有洛朗级数形式的解,其中变量满足一阶微分方程。通过齐次平衡法,确定出两个参数n和r;代入方程,比较同次幂项的系数,将非线性方程组的求解问题转化为代数方程组的求解;得出了含色散方程组的孤子解、有理解、三角函数周期解和Jacobi椭圆函数双周期解。相比于其他方法,这种基于符号计算的代数方法,可更快速、高效地求出非线性方程多种不同类型的精确解。
In order to find an appropriate method for solving the dispersive long wave equations,we use an algebraic method based on symbolic computation proposed by Fan En’gui in integrable systems and computer algebra to construct soliton solutions,rational number solutions and periodic solutions of nonlinear equations.On the basis of travelling wave transformation,it is assumed that the equation has a solution in the form of Laurent series,in which the variables satisfy the first order differential equation.Through homogeneous balance method,the two parameters n and r are determined;the solution of nonlinear equations is transformed into the solution of algebraic equations by substituting into the equation and comparing the coefficients of the same power term;the soliton solutions,rational number solutions,periodic solutions of trigonometric functions and biperiodic solutions of Jacobi elliptic functions are obtained.Compared with other methods,this algebraic method based on symbolic computation can find many kinds of exact solutions of nonlinear equations more quickly and efficiently.
作者
陈南
CHEN Nan(College of Computer and Artificial Intelligence, Xiamen Institute of Technology, Xiamen, Fujian 361021, China)
出处
《闽江学院学报》
2021年第2期7-12,共6页
Journal of Minjiang University
基金
福建省中青年教师教育科研项目(JAT190958)
厦门工学院校级科研基金项目(KYT2019021)。
关键词
含色散长波方程组
行波变换
孤子解
有理解
周期解
long wave equations with dispersion
traveling wave transformation
soliton solutions
rational number solutions
periodic solutions
