Unnormalized modified KdV equation

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

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

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

This is a special case of the Gardner equation.

References

Andrei D. Polyanin, Valentin F. Zaitsev, Handbook of Nonlinear Partial Differential Dquations, second edition p. 870 CRC PRESS

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

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