伊藤方程(Ito equation)是一个五阶非线性偏微分方程：

U_{t}+((6U^5+10\alpha(U^2U_{xx}+U*U_{x}^2)+U_{xxxx})_{x}=0

解析解
:u(x, t) = _C2sech(_C1+_C2x-_C2^5*t)
:u(x, t) = _C3JacobiDN(-_C2-_C3x-(-6_C3^5-_C3^5_C1^4+6_C3^5_C1^2)*t, _C1)
:u(x, t) = \sqrt(2)_C3JacobiCN(_C2+_C3x-7_C3^5t, (1/2)sqrt(2))
:u(x, t) = -I_C2cot(_C1+_C2x-6_C2^5*t)
:u(x, t) = -I_C2tan(_C1+_C2x-6_C2^5*t)
:u(x, t) = -I_C3JacobiNS(-_C2-_C3x-(-_C3^5_C1^4-_C3^5-4_C3^5_C1^2)*t, _C1)
:u(x, t) = I_C2csc(_C1+_C2x-_C2^5t)
:u(x, t) = (2I)_C3JacobiND(_C2+_C3x-28_C3^5t, sqrt(2))
:u(x, t) = -Isqrt(2)_C3JacobiNC(_C2+_C3x-7_C3^5t, (1/2)*sqrt(2))
:u(x, t) = -2_C3JacobiSN(_C2+_C3x-28_C3^5*t, I)
:u(x, t) = -\sqrt(1-_C1^2)_C3JacobiND(-_C2-_C3x-(-6_C3^5-_C3^5_C1^4+6_C3^5_C1^2)t, _C1)

行波图
参考文献

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