Klein-Gordon Equation

The partial differential equation

(1)

that arises in mathematical physics.

The quasilinear Klein-Gordon equation is given by

(2)

(Nayfeh 1973, p. 76; Zwillinger 1997, p. 133), and the nonlinear Klein-Gordon equation by

(3)

(Matsumo 1987; Zwillinger 1997, p. 133).

REFERENCES:

Matsumo, Y. "Exact Solution for the Nonlinear Klein-Gordon and Liouville Equations in Four-Dimensional Euclidean Space." J. Math. Phys. 28, 2317-2322, 1987.

Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I. New York: McGraw-Hill, p. 272, 1953.

Nayfeh, A. H. Perturbation Methods. New York: Wiley, 1973.

Zwillinger, D. Handbook of Differential Equations, 3rd ed. Boston, MA: Academic Press, pp. 129 and 133, 1997.