Kuramoto-Sivashinsky 方程是一个非线性常微分方程: 此方程的解析解为 其中.利用阿多米安分解法可求得Kuramoto-Sivashinsky 方程的柯西问题近似解. 初始条件 u(0)=sin(x); pa:= (2441*sin(6.*x)+0.1693e-1*sin(4.*x)-0.5787e-4*sin(2.*x)5382*sin(10.*x)+.7224*sin(8.*x))*t^9+(.1514*sin(5.*x)+0.1356e-5*sin(x)+.4634*sin(9.*x)5585*sin(7.*x)-0.5933e-2*sin(3.*x))*t^8+(-0.8889e-1*sin(4.*x)4063*sin(8.*x)+0.1389e-2*sin(2.*x)+.4339*sin(6.*x))*t^7+(.3647*sin(7.*x)3391*sin(5.*x)-0.1085e-3*sin(x)+0.4746e-1*sin(3.*x))*t^6+(3375*sin(6.*x)-0.2083e-1*sin(2.*x)+.2667*sin(4.*x))*t^5+(2109*sin(3.*x)+0.5208e-2*sin(x)+.3255*sin(5.*x))*t^4+(3333*sin(4.*x)+.1667*sin(2.*x))*t^3+(1250*sin(x)+.3750*sin(3.*x))*t^25000*t*sin(2.*x)+sin(x)