Modified Korteweg-De Vries equation explained

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

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

where

\alpha is an arbitrary (nonzero) constant.

This is a special case of the Gardner equation.

See also

• Korteweg–de Vries equation

References

• Book: Griffiths, Graham W. . Schiesser . W. E. . Traveling Wave Analysis of Partial Differential Equations . Academic Press . Amsterdam; Boston . 2011 . 978-0-12-384652-5 . 657600287.
• Book: Polyanin, Andrei D. . Zaitsev . Valentin F. . Handbook of Nonlinear Partial Differential Equations . Chapman and Hall/CRC . Boca Raton, Fla . 2003-10-29 . 978-1-58488-355-5. 9.1.2. Cylindrical, Spherical, and Modified Korteweg-de Vries Equations.