Korteweg-de Vries-Burgers' equation explained

The Korteweg-de Vries–Burgers equation is a nonlinear partial differential equation:

u _{t+\alpha} u _{xxx} + uu _{x} - \beta u _{xx} =0 .

The equation gives a description for nonlinear waves in dispersive-dissipative media by combining the nonlinear and dispersive elements from the KdV equation with the dissipative element from Burgers' equation.

The modified KdV-Burgers equation can be written as:

u _{t+} a u _{xxx} + u ^{2 u} _{x} - b u _{xx} =0 .

See also

• Burgers' equation
• Korteweg–de Vries equation
• modified KdV equation

References

• Book: Polyanin, Andrei D. . Zaitsev . Valentin F. . Handbook of Nonlinear Partial Differential Equations . Chapman and Hall/CRC . Boca Raton, Fla . 2003 . 978-1-58488-355-5. 9.1.7. Burgers–Korteweg–de Vries Equation and Other Equation.
• Wang . Mingliang . Exact solutions for a compound KdV-Burgers equation . Physics Letters A . 213 . 5-6 . 1996 . 10.1016/0375-9601(96)00103-X . 279–287.