Quasi-periodic waves and asymptotic behavior for a coupled nonlinear Klein-Gordon equation

Abstract

With the Hirota’s bilinear method, N N -periodic wave solutions to the coupled nonlinear Klein-Gordon equation are constructed in terms of theta function. The asymptotic behaviors under small amplitude limits are also deduced strictly for the one and two-periodic waves. Moreover, a numerical scheme is presented for the case of N ≥ 3 N\geq 3 . Some three-periodic wave solutions are calculated numerically as examples.