基于KdV近似和Runge-Kutta数值方法的Toda孤立子系统非匹配特性研究

Mismatch Characteristics of Toda Soliton System Based on KdV Approximation and Runge-Kutta Numerical Method

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 soliton has demonstrated its existence and application in many different science and engineering fields. The mismatch characteristics of the nonlinear system to which Toda soliton corresponds seriously affects the performance of soliton system. In this paper, KdV approximation and Runge-Kutta methods are applied to study the response problem of the mismatched Toda soliton system. For different mismatch coefficients and input signal amplitudes, the effects of system mismatch on output amplitude and phase are studied and the changes of output variables are described quantitatively. Theoretical analysis and simulation results show that in the case of small mismatch coefficients and small input amplitudes, the system mismatch distorts the signal phase only, and has bo influence on the input amplitude, while, in the case of large mismatch coefficients and large input amplitudes, the system mismatch distorts both the signal amplitude and phase.