(3+1)维非线性Burgers系统的新的分离变量解及其局域激发结构与分形结构

New variable separation solutions,localized structures and fractals in the (3+1)-dimensional nonlinear Burgers system

将扩展的Riccati方程映射法推广到了(3+1)维非线性Burgers系统,得到了系统的分离变量解;由于在解中含有一个关于自变量(x,y,z,t)的任意函数,通过对这个任意函数的适当选取,并借助于数学软件Mathematica进行数值模拟,得到了系统的新而丰富的局域激发结构和分形结构.结果表明,扩展的Riccati方程映射法在求解高维非线性系统时,仍然是一种行之有效的方法,并且可以得到比(2+1)维非线性系统更为丰富的局域激发结构.

Applying the extended Riccati mapping approach to the （3 ＋ 1）-dimensional nonlinear Burgers system, we obtain new variable separation solutions which contain an arbitrary function. With the help of numerical simulation of Mathematica, abundant special types of new localized excitations and fractals are discussed by selecting the arbitrary function appropriately. The solutions indicate that the extended Riccati mapping approach is valid for solving a class of （3 ＋ 1 ）-dimensional nonlinear equations and can obtain much more abundant localized excitations than that of the （2 ＋ 1）-dimensional nonlinear equations.