Circuit implementations of soliton systems

Recently, a large class of nonlinear systems which possess soliton solution s has been discovered for which exact analytic solutions can be found. Soli tons are eigenfunctions of these systems which satisfy a form of superposit ion and display rich signal dynamics as they interact. In this paper, we vi ew solitons as signals and consider exploiting these systems as specialized signal processors which are naturally suited to a number of complex signal processing tasks. New circuit models are presented for two soliton systems , the Toda lattice and the discrete-KdV equations. These analog circuits ca n generate and process soliton signals and can be used as multiplexers and demultiplexers in a number of potential soliton-based wireless communicatio n applications discussed in [Singer et al.]. A hardware implementation of t he Toda lattice circuit is presented, along with a detailed analysis of the dynamics of the system in the presence of additive Gaussian noise. This ci rcuit model appears to be the first such circuit sufficiently accurate to d emonstrate true overtaking soliton collisions with a small number of nodes. The discrete-KdV equation, which was largely ignored for having no prior e lectrical or mechanical analog, provides a convenient means for processing discrete-time soliton signals.