Seventh-order Korteweg–de Vries equation

The seventh-order KdV equation is a nonlinear partial differential equation in 1+1 dimensions related to the KdV equation.^[1] It is defined by the formula

$u_{t}+6uu_{x}+u_{{xxx}}-u_{{xxxxx}}+\alpha u_{{xxxxxxx}}=0.$

where $x$ and $t$ are real variables and $\alpha$ is a constant.

References

1. Andrei D. Polyanin,Valentin F. Zaitsev, Handbook of Nonlinear Partial Differential Equations, Second Edition, SECOND EDITION p. 1040 CRC PRESS