Unnormalized modified KdV equation

The unnormalized modified Korteweg–de Vries (KdV) equation is an integrable nonlinear partial differential equation：^[1]

${\displaystyle u_{t}+u_{xxx}+\alpha u^{2}u_{x}=0\,}$

where ${\displaystyle \alpha }$ is an arbitrary (nonzero) constant. See also Korteweg–de Vries equation.

This is a special case of the Gardner equation.

References[]

• Graham W. Griffiths, William E. Shiesser Traveling Wave Analysis of Partial Differential Equations, Academy Press