The Nonlinear Universe – Solitons and Chaos

In this article, two of the pinnacles of nonlinear science – solitons and chaos, are discussed giving importance to the philosophy behind these concepts, and highlighting the ubiquity of the duo in real life phenomena. It is seen that solitons and chaos are prevalent in nature much more than one would expect, and are much wider in scope than the restrictive mathematical equations usually seen in literature. While solitons are a representation of the fundamental life cycle of birth, growth, zenith, decay and death, chaos is seen as a representation of the amount of information an observer possesses, and the interconnectedness between everything and everything else. Various applications of the soliton in communications and computing are discussed. The smoothness and compactness of the soliton give rise to its involvement in various phenomena in nature, along with the genesis of the ‘solitary wavelet’. With the characteristic signatures of determinism and sensitive dependence on initial conditions, chaos theory forms the hallmark of nonlinear science. The present work stresses on and elaborates various techniques on achieving an easy-to-tune signal based chaos, with the help of standard circle maps, mathematical functions and digital circuits. Following this various applications of chaos theory are discussed, culminating in a chaotic interpretation of quantum mechanics and Theory of Everything. Finally, nonlinear analysis and its significance in various real time data are outlined with suitable examples and illustrations.