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Kadomtsev-Petviashvili equation

Kadomtsev-Petviashvili equation
Order4th
SolvableExactly solvable

Contents

Definition

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

x ( u t +u u x +β u xxx )+3 δ 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

  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

External links

  1. Kadomtsev-Petviashvili equation in Wikipedia, the free encyclopedia
  2. Kadomtsev-Petviashvili equation in Wolfram MathWorld
  3. Kadomtsev-Petviashvili equation in Scholarpedia

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