DP 方程(Degasperis-Procesi equation)是一个模拟弥散介质中非线性波动非线性偏微分方程：

\displaystyle u_t - u_{xxt} + 2\kappa u_x + 4u u_x = 3 u_x u_{xx} + u u_{xxx}

解析解
DP方程有解析解

A(x) := b^3+3b^3\frac{(\frac{(1-(1/4)p^2)}{(1-p^2)}-1)(\frac{(4(1-(1/4)p^2)}{(1-p^2)}-1)}{((2\frac{(1-(1/4)p^2))}{(1-p^2)}-1+\sqrt{\frac{(1-(1/4)p^2}{(1-p^2))}}cosh(x))}

B(x,t) := \frac{x}{p}+4a^2t+log(\frac{(\alpha+1+exp(x(\alpha-1)))}{(alpha-1+(e)^(x (\alpha+1)))})

其中

alpha := \frac{((2a-1)(a+1)}{((2a+1)(a-1)))^(1/2)}

代入，

取参数p = .3, b = 1.1

A(x)=1.331+\frac{.9764}{(1.148+1.036*cosh(x))}

B(x,t)=3.33x+4.2967t+ln(\frac{(5.418+exp(3.418x))}{(3.418+exp(5.4181x))})

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