阶跃初值条件解的完全分类: 流体力学中广义 Gardner 方程的分析与数值验证

张岩,郝惠琴,郭睿

The Complete Classification of Solutions to the Step Initial Condition: Analysis and Numerical Verification for the Generalized Gardner Equation in Fluid Mechanics

Yan Zhang,Huiqin Hao,Rui Guo

图37 区域 2 $ \sim $ 区域 4 黎曼不变量 $ R_i $ 的解析解, 参数如下: (a) $ k_1 =12 $, $ k_2 =4 $, $ d =4 $, $ u^- =1 $, $ u^+ =-6 $, (b) $ k_1 =6 $, $ k_2 =3 $, $ d =8 $, $ u^- =1 $, $ u^+ =-2 $, (c) $ k_1 =8 $, $ k_2 =2 $, $ d =2 $, $ u^- =3 $, $ u^+ =-1 $. 图中分别显示的是 $ t = 1, 5, \frac{1}{2} $ 时的情况.