Order4th
SolvableExactly solvable

## Definition

The Kadomtsev-Petviashvili equation (KP equation for short) is a nonlinear partial differential equation wich can be written as follows

$\frac{\partial }{\partial x}\left({u}_{t}+u{u}_{x}+\beta {u}_{xxx}\right)+3{\delta }^{2}{u}_{yy}=0$

## History

The KP equation was first introduced by Kadomtsev and Petviashvili in 1970.

## References

1. Kudryashov N.A. Analytical theory of nonlinear differential equations (in Russian) // 2nd ed., Institute of Computer Investigation, Moscow-Izhevsk, 2004. — 360 p.
2. Kudryashov N.A. Methods of nonlinear mathematical physics (in Russian) // Moscow Engineering Physics Institute, Moscow, 2008. — 352 p.
3. Weiss J. Modified equations, rational solutions, and the Painlevé property for the Kadomtsev-Petviashvili and Hirota-Satsuma equations // J. Math. Phys., 1985. 26:9. Pp.2174 – 2180. DOI:10.1063/1.526841