Soliton solutions of coupled nonlinear Klein–Gordon equations

The coupled nonlinear Klein–Gordon equations are analyzed for their integrability properties in a systematic manner through Painlevé test. From the Painlevé test, by truncating the Laurent series at the constant level term, the Hirota bilinear form is identified, from which one-soliton solutions are derived. Then, the results are generalized to the two, three and N-coupled Klein–Gordon equations.