Seventh-order Korteweg–De Vries equation

The seventh-order Korteweg–De Vries equation is a nonlinear partial differential equation in 1+1 dimensions related to the KdV equation.^[1] It is defined by the formula ${\displaystyle u_{t}+6uu_{x}+u_{xxx}-u_{xxxxx}+\alpha u_{xxxxxxx}=0.}$ where ${\displaystyle x}$ and ${\displaystyle t}$ are real variables and ${\displaystyle \alpha }$ is a constant.

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