BILINEAR FORM AND SOLITON SOLUTIONS FOR THE COUPLED NONLINEAR KLEIN–GORDON EQUATIONS

With the coupling of a scalar field, a generalization of the nonlinear Klein–Gordon equation which arises in the relativistic quantum mechanics and field theory, i.e., the coupled nonlinear Klein–Gordon equations, is investigated via the Hirota method. With the truncated Painlevé expansion at the constant level term with two singular manifolds, the coupled nonlinear Klein–Gordon equations are transformed to a bilinear form. Starting from the bilinear form, with symbolic computation, we obtain the N-soliton solutions for the coupled nonlinear Klein–Gordon equations.