含可积系统的变系数(2+1)维破裂孤立子方程的拟周期解计算研究  

Study on Quasi-periodic Solution of (2+1)-dimensional Fractal Soliton Equations with Variable Coefficients

作　　者：黄杰英 

机构地区：[1]商丘学院计算机工程学院,河南商丘476000

出　　处：《科技通报》2017年第6期18-21,共4页Bulletin of Science and Technology

摘　　要：为了能够使相关事物间的关系更加明确地表现出来,文中以含可积系统的变系数(2+1)维破裂孤立子方程为研究对象,对该方程进行拟周期解计算。首先,运用多指数法借助指数函数的线性微分关系,将非线性演化方程的求解问题转换为非线性代数方程组的求解问题,通过求解计算非线性代数方程组获取结果,将计算结果代回到原来变量方程中,形成新的非线性方程;然后,将利用多指数法构造完成的孤立子方程与Riemann函数法相结合,并产生拟周期波解的计算方法,通过引入Riemann函数表示线性微分方程再经过B?cklund变换,得到变系数(2+1)维孤立子演化方程的双拟周期波解。仿真实验证明,运用文中方法对含可积系统的变系数(2+1)维破裂孤立子方程有效地完成了拟周期解计算。In order to be able to make the relationship between the related things more clearly, this paper takes the variable coefficient(2+1) dimensional breaking soliton equation with integrable system as the research object. First of all, by means of linear differential relationship of exponential function with multi index, the nonlinear evolution equation for the conversion problem solving nonlinear algebraic equations,nonlinear algebraic equations obtained by solving the calculation results, the results back to the original generation of variable equation, the formation of new nonlinear equations; then, the combination of soliton the equation and the Riemann function will use the multi index method constructed, and quasi periodic wave solutions of calculation method, by introducing the Riemann function representation of linear differential equations after B by cklund transform, obtain variable coefficient(2+1) equation of quasi periodic wave solutions of two dimensional soliton evolution. The simulation results show that the proposed method can effectively calculate the quasi periodic solutions of the variable coefficient(2+1)-dimensional fracture soliton equation with integrable system.

关 键 词：破裂孤立子方程 多指数法 拟周期解计算 

分 类 号：O178[理学—数学]