Existence of solution for carleman equation by finite difference method

Abstract

The Carleman equation is the coupled system of first order hyperbolic nonlinear equations $u_t+u_x=v^2-u^2$ $v_t-v_x=u^2-v^2$ We have the constructive proof of the existence of a solution for the initial value problem of Carleman equation defined on the domain R × [0, ∞) by a finite difference method.