Korteweg-de Vries-Burgers' equation

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

${\displaystyle u_{t}+\alpha u_{xxx}+uu_{x}-\beta u_{xx}=0.}$

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.^[1]

The modified KdV-Burgers equation can be written as:^[2]

${\displaystyle u_{t}+au_{xxx}+u^{2}u_{x}-bu_{xx}=0.}$

See also

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

Notes

1. Polyanin & Zaitsev 2003.
2. Wang 1996.

References

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