Exciton and phonon propagation in lower and higher dimensional pro tein molecular systems

Abstract

Nonlinear dynamics is mainly concerned with the study of integrable and newlinenon-integrable systems. Ironically, the concept of integrability is not well defined newlineand there seems to be no precise definition of it yet. One possibility out of the newlineexisting many possibilities is the literal meaning, that is the corresponding non- newlinelinear differential equation is integrable means that it can be integrated with the newlinerequired number of arbitrary(integration) constants/functions and posses infinite newlinenumber of conservation laws. Integrable nonlinear systems with infinite degrees newlineof freedom often have the famous soliton solutions. Solitons are localized trav- newlineelling waves first discovered in shallow water. They are ubiquitous and exist in newlinemany kinds of systems from the sky to the laboratory, from physical to biological newlinesystems. The non integrable systems in general exhibit irregular, aperiodic and newlinechaotic behaviour with solutions having complicated singularity structure in the newlinecomplex time plane. The irregular and unpredictable time evolution of many newlinenonlinear systems is typically called chaos. Chaotic phenomenon, which occurs newlineonly when the governing equations are nonlinear, is known as sensitivity to initial newlineconditions. newline