The partial differential equation 1/c^2 (d^2 ψ)/(dt^2) = (d^2 ψ)/(dx^2) - μ^2 ψ that arises in mathematical physics. The quasilinear Klein-Gordon equation is given by u_(t t) - α^2 u_(x x) + γ^2 u = β u^3 (Nayfeh 1973, p. 76; Zwillinger 1997, p. 133), and the nonlinear Klein-Gordon equation by sum_(i = 1)^n u_(x_i x_i) + λ u^p = 0 (Matsumo 1987; Zwillinger 1997, p. 133).

Liouville's equation | sine-Gordon equation | wave equation