Toda晶格电路中孤子信号的矩形脉冲激发方法  

Excitation of Solitons by Using Rectangular Pulses in the Toda Lattice Circuit

作　　者：梅笑冰[1] 王新龙[1] 

机构地区：[1]南京大学近代声学国家重点实验室声学研究所,南京210093

出　　处：《南京大学学报（自然科学版）》2005年第3期318-324,共7页Journal of Nanjing University（Natural Science）

基　　金：国家杰出青年科学基金(19925414);国家自然科学基金(10074032);"973"国家基础研究计划重大项目的支持

摘　　要：　通过电-力类比可以建立与Toda晶格系统等价的电路,利用电路产生的孤子信号可以进行一些特殊的信号处理,使用非线性的方法对信号进行调制解调.通过数值计算,研究了在各种幅度和宽度矩形脉冲激励下,Toda晶格电路中孤子激发的情况.使用矩形脉冲,可以根据调制解调信号的需要激发出单孤子、双孤子直至多孤子.同时也可以根据矩形脉冲激发孤子的规律来设计发送端多孤子的产生,使其合成后的复合信号可用相应的矩形脉冲代替,减小系统的复杂度和传输系统的码率.<Abstrcat> Traditional signal processing and communication rely on the linear models of underlying systems. However, nonlinear models and the corresponding methods hold the potential to provide more efficient algorithms and applications for a variety of signal processing and communication problems where linear techniques are suboptimal. The class of nonlinear systems that have soliton solutions appears to be one of the nonlinear systems. Solitons are eigenfunctions of some nonlinear evolution equations. They possess some unique features, say, maintaining constant shape and velocity during propagation, and the nonlinear superposition of multiple solitons in the course of interactions, etc. All these may be applied to some specific tasks of signal processing and communication. For example, one can decompose complex solutions to a spectrum of soliton signals, each of which has some simple dynamic structures, and view these soliton signals as carriers to implement signal modulation and demodulation.The Toda lattice circuit is a circuit implementation of the Toda lattice system which has soliton solutions. In the real circuit implementation, it becomes necessary to answer the following question: how can we generate or excite a given form of soliton signals in the circuit? In principle, the inverse scattering theory can be used to solve this problem mathematically. However, the procedure will be too complicated to be put into practice. In this paper, we explore this problem via numerical simulations, and try to find a relatively simple way to excite the desired waveforms of solitons. In experiment, rectangular pulses are among the most available electronic waveforms that can be easily generated by various common electronic instruments. We therefore focus our attention on the excitation of solitons by using rectangular pulses. We find that a pure soliton signal can be formed if the input rectangular pulse takes after the so-called standard waveform, i.e., the rectangular pulse has the same height and width as that of th

关 键 词：TODA晶格 非线性电路 矩形脉冲 孤子激发 调制解调 

分 类 号：O322[理学—一般力学与力学基础] TM13[理学—力学]