Kadomtsev-Petviashvili Equation

The partial differential equation

(1)

where

(2)

(Krichever and Novikov 1980; Novikov 1999). Zwillinger (1997, p. 131) and Calogero and Degasperis (1982, p. 54) give the equation as

(3)

The modified Kadomtsev-Petviashvili equation is given by

(4)

(Clarkson 1986; Zwillinger 1997, p. 133).

REFERENCES:

Baker, H. F. Abelian Functions: Abel's Theorem and the Allied Theory, Including the Theory of the Theta Functions. New York: Cambridge University Press, p. xix, 1995.

Calogero, F. and Degasperis, A. Spectral Transform and Solitons: Tools to Solve and Investigate Nonlinear Evolution Equations.New York: North-Holland, 1982.

Clarkson, P. A. "The Painlevé Property, a Modified Boussinesq Equation and a Modified Kadomtsev-Petviashvili Equation." Physica D 19, 447-450, 1986.

Krichever, I. M. and Novikov, S. P. "Holomorphic Bundles over Algebraic Curves, and Nonlinear Equations." Russ. Math. Surv. 35, 53-80, 1980. English translation of Uspekhi Mat. Nauk 35, 47-68, 1980.

Novikov, D. P. "Algebraic-Geometric Solutions of the Krichever-Novikov Equation." Theoret. Math. Phys. 121, 1567-15773, 1999.

Zwillinger, D. Handbook of Differential Equations, 3rd ed. Boston, MA: Academic Press, p. 131, 1997.