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潘陈蓉,陈松林.Klein-Gordon波动方程多波传播的非线性特性
Nonlinear characteristics of multi-wave propagation in Klein-Gordon wave equation[J].计算力学学报,2020,37(5):646~650
Klein-Gordon波动方程多波传播的非线性特性
Nonlinear characteristics of multi-wave propagation in Klein-Gordon wave equation
Nonlinear characteristics of multi-wave propagation in Klein-Gordon wave equation
投稿时间:2020-01-19  修订日期:2020-05-09
DOI:10.7511/jslx20200119001
中文关键词:  非线性波动方程  多波传播  多尺度展式  首项近似  非线性特性  相速
英文关键词:nonlinear wave equation  multi-wave propagation  multi-scale expansion  leading-term approximation  nonlinear characteristic  phase velocity
基金项目:安徽省高校自然科学研究重点(KJ2019A0062)资助项目.
作者单位E-mail
潘陈蓉 安徽工业大学 数理科学与工程学院, 马鞍山 243002  
陈松林 安徽工业大学 数理科学与工程学院, 马鞍山 243002 slchen@ahut.edu.cn 
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中文摘要:
      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)。
英文摘要:
      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.
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