伯格斯方程（Burgers equation）是一个模拟冲击波的传播和反射的非线性偏微分方程，給定函數 
，與擴散係數 
，則一維的伯格斯方程可以寫成以下的形式:
伯格斯方程通过下列Backlund变换[1]。
![{\displaystyle w[x]={\frac {1}{2}}wu}](//wikimedia.org/api/rest_v1/media/math/render/svg/8a81e71b8e6a9b2d0bab5a68aabef873ebe48949)
![{\displaystyle w[t]={\frac {1}{2}}w[x]u+{\frac {1}{2}}wu[x]}](//wikimedia.org/api/rest_v1/media/math/render/svg/e9b0a5d9f79f3a81a1ef2b2149cb6a9a0e658f76)
则化为 热方程：
![{\displaystyle HEq:=w[t]=w[x,x]}](//wikimedia.org/api/rest_v1/media/math/render/svg/284bd3db109e496f31aca22e271d172564e7ec88)
Inna Shingareva, Carlos Lizarraga Celaya, Solving Nonlinear Differential Equations with Maple and Mathematica, p47,Springer
Inna Shingareva, Carlos Lizárraga-Celaya,Solving Nonlinear Partial Differential Equations with Maple p57-58Springer
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![{\displaystyle w[x]={\frac {1}{2}}wu}](http://wikimedia.org/api/rest_v1/media/math/render/svg/8a81e71b8e6a9b2d0bab5a68aabef873ebe48949)
![{\displaystyle w[t]={\frac {1}{2}}w[x]u+{\frac {1}{2}}wu[x]}](http://wikimedia.org/api/rest_v1/media/math/render/svg/e9b0a5d9f79f3a81a1ef2b2149cb6a9a0e658f76)
![{\displaystyle HEq:=w[t]=w[x,x]}](http://wikimedia.org/api/rest_v1/media/math/render/svg/284bd3db109e496f31aca22e271d172564e7ec88)
