基于一维高阶非线性波模型,用动力系统定性分析法分析了微结构固体中扭结与反扭结孤立波存在的可能性及其存在条件.分析结果表明:适当条件下高阶非线性和反常频散的微结构固体中可存在扭结和反扭结孤立波,准确给出了这些孤立波的存在条件.用数值方法分析了微结构固体的高阶微尺度非线性效应对扭结与反扭结孤立波的影响.结果表明:随着高阶微尺度非线性效应的负增强(或正增强),扭结与反扭结孤立波变得越来越陡峭(或平缓),但其幅度保持不变.
Based on one dimensional high-order nonlinear wave model,the possibility and existence condition of kink and anti-kink solitary waves in microstructured solids are analyzed with the qualitative analysis method of dynamic system.Analysis results show that the kink and anti-kink solitary waves can exist in high-order nonlinear and anomalous dispersion microstructured solids under appropriate conditions,and the existence conditions are given exactly.Influences of high-order microscale nonlinear effect on the kink and anti-kink solitary waves are analyzed with the numerical method.Results show that the kink and anti-kink solitary waves become more and more steep (or gentle) with the negative reinforcing (or positive reinforcing) of high-order microscale nonlinear effect,while their amplitudes remain unchanged.
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