### From Neqwiki, the nonlinear equations encyclopedia

# Kadomtsev-Petviashvili equation

Kadomtsev-Petviashvili equation | |
---|---|

Order | 4th |

Solvable | Exactly solvable |

## Contents |

## 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.## Solutions

### Type of a solution

## Integrals of motion

## Lax pairs

## Lagrangian

## Hamiltonian

## Applications and connections

## Variations

## See also

## References

- Kudryashov N.A.
*Analytical theory of nonlinear differential equations*(in Russian) // 2^{nd}ed., Institute of Computer Investigation, Moscow-Izhevsk, 2004. — 360 p. - Kudryashov N.A.
*Methods of nonlinear mathematical physics*(in Russian) // Moscow Engineering Physics Institute, Moscow, 2008. — 352 p. - 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

## External links

- Kadomtsev-Petviashvili equation in Wikipedia, the free encyclopedia
- Kadomtsev-Petviashvili equation in Wolfram MathWorld
- Kadomtsev-Petviashvili equation in Scholarpedia