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| Nonlinear characteristics of multi-wave propagation in Klein-Gordon wave equation |
| Received:January 19, 2020 Revised:May 09, 2020 |
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| DOI：10.7511/jslx20200119001 |
| KeyWord:nonlinear wave equation multi-wave propagation multi-scale expansion leading-term approximation nonlinear characteristic phase velocity |
| Author | Institution |
| 潘陈蓉 |
安徽工业大学 数理科学与工程学院, 马鞍山 |
| 陈松林 |
安徽工业大学 数理科学与工程学院, 马鞍山 |
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| Abstract: |
| 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. |