Cellular nonlinear Networks Meet KdV equation: a New Paradigm

Abstract: The Korteweg-deVries equation, used to describe long and solitary wave propagation on shallow water, later called soliton, besides describing phenomena ranging from the dynamics of plasmas to tsunami can be implemented into Cellular Neural Networks (CNNs), analog circuit which processes signals in real time with the aim to create a completely innovative generation of trasmission lines and a new mtehod for studying wave-like propagation of information in multidimensional nonlinear and dispersive media. In this paper, after a short presentation of both systems, we empirically verify that the behavior of the KdV can be emulated by CNNs. As the PDEs dynamics and its associated CNN equation have identical solutions, the integrated system can be considered a physical model, able to generate soliton-like behavior, giving rise to computing machines based on non-linear dynamics. Interestingly, their way of encoding and conveying information is very similar to that of biological systems.