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Toda孤立子广泛存在于不同科学及工程领域,并具有广阔应用前景。Toda孤立子所对应的非线性系统的非匹配特性将对基于Toda孤立子的系统性能产生严重影响。文章采用KdV近似方法及Runge-Kutta数值方法,研究非匹配情况下Toda孤立子非线性系统的响应问题。针对不同非匹配系数及输入信号幅度,研究非匹配特性对系统输出信号幅度及相位的影响,并给出输出幅度及相位随时间的变化与电路非匹配系数之间的定量关系。理论分析及仿真结果证实在较小输入幅度及较小电路非匹配系数情况下,Toda电路的非匹配只会导致孤立子的输出相位的失真而不会造成幅度抖动。在较大输入幅度及较大电路非匹配情况下,孤立子的输出相位及幅度均产生较大失真。
Toda solitons exist widely in different fields of science and engineering, and have broad application prospects. The non-matching nature of the nonlinear system corresponding to the Toda soliton will have a serious impact on the system performance based on the Toda soliton. In this paper, KdV approximation method and Runge-Kutta numerical method are used to study the response of Toda soliton nonlinear systems under non-matching conditions. According to the different unmatched coefficients and the amplitude of the input signal, the influence of the unmatched characteristic on the amplitude and phase of the output signal of the system is studied. The quantitative relationship between the output amplitude and the phase variation with time and the unmatched coefficient of the circuit is given. The theoretical analysis and simulation results show that the Toda circuit’s mismatch will only result in distortion of the output phase of the soliton without amplitude jittering at a small input amplitude and smaller circuit non-matching coefficients. In the case of larger input amplitude and larger circuit mismatch, the output phase and amplitude of the soliton have larger distortion.