Klein-Gordon Equation

The partial differential equation


that arises in mathematical physics.

The quasilinear Klein-Gordon equation is given by


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


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

See also

Liouville's Equation, Sine-Gordon Equation, Wave Equation

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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.

Referenced on Wolfram|Alpha

Klein-Gordon Equation

Cite this as:

Weisstein, Eric W. "Klein-Gordon Equation." From MathWorld--A Wolfram Web Resource.

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