关键词: Klein-Gordon方程, 山路引理, 行波解的存在性, 加权的能量估计, 行波解的渐近稳定性

Abstract: Firstly, we proved the existence of  traveling wave solutions for Klein-Gordon equations with complex nonlinear source terms by using the mountain pass lemma. Secondly, we proved that the  traveling wave solution of the equation had asymptotic  stability  by using the perturbation function method and the weighted  energy estimate method under the initial conditions.

Key words: Klein-Gordon equation, mountain pass lemma, existence of , traveling wave solution, weighted , energy estimate, asymptotic , stability of , traveling wave solution