Klein-Gordon波动方程多波传播的非线性特性

基于双波初值问题，讨论非线性对多波传播的影响。通过选取合适的多重尺度，对Klein-Gordon波动方程进行变形，得到方程的解的多尺度展式首项近似和三波传播时速度相互影响的定量关系，揭示了多波传播的非线性特性；最后，应用Mathematica对波动方程进行数值仿真。研究结果表明，另外多个波的存在会使波的传播速度（相速）超过独自传播时的速度（相速）。

Nonlinear characteristics of multi-wave propagation in Klein-Gordon wave equation

The influence of nonlinearity on multi-wave propagation was discussed based on the study of the two-wave initial value problem.By choosing appropriate multiple scales and deforming Klein-Gordon wave equation,the multi-scale extended first term approximation of the solution of the equation and the quantitative relationship between the influence of three-wave propagation velocity were obtained, which revealed the nonlinear characteristics of multi-wave propagation.Finally,the wave equation was solved numerically in Mathematica.The research results showed that the existence of additional multiple waves would make the propagation speed (phase velocity) of wave exceed the speed (phase velocity) that it propagated alone.