Regular solutions of the Liouville equation

For the Liouville equation $\varphi_{tt}(t,x)-\varphi_{xx}(t,x)\pm(m^2/2)e^{\varphi(t,x)}=0$ the Goursat problem is solved explicitly and the properties of regular solutions are investigated. The Liouville equation is regarded as a model of a self-interacting scalar field. The asymptotic fields, the classical $S$ matrix, and observable quantities such as the energy and momentum are constructed.