具對流與擴散項之非線性Burgers 方程，已有熟知之Cole-Hopf 變換解法，而本文採用相似法直接
在物理面上探討Burgers 方程，並有系統地以伸縮群及行波相似轉換求得其相似精確解並加以應用在
氣動力學中之膨脹波與激波問題。
本文再以適當的起始條件求出Cole-Hopf 變換解，並與本文相似解加以連結，使吾人對Burgers 方
程之數學結構與物理意義有更進一步之認識和了解。 The prototype equation for nonlinear convection-diffusion processes is Burgers' equation. An analytical
solution of Burgers' equation was discovered independently by Cole and Hopf.
In this paper, a similarity study of Burgers' equation is exhibited. A systematic approach for obtaining
the stretching group and traveling wave similarity solutions are constructed and applied to gas-dynamic
problems.
Some exact solutions are also obtained from Cole-Hopftransformation and they are related to the similarity
solutions of stretching group and traveling wave.
