Nonlinear Science, Emergence & Dynamics of Coherent Structures

The study of nonlinear systems has quietly revolutionized the realm of science. Models of physical phenomena had previously been assumed to be linear, or nearly so. This allowed the construction of equations which were relatively simple to solve. It has, however, become increasingly evident that this assumption of linearity leads the theorist to miss qualitatively significant phenomena. For nonlinear systems, it is now known, the whole is greater than the sum of its parts, leading to the emergence of new structures that have their own features, lifetimes and peculiar ways of interacting. Since these interactions are also nonlinear, new dynamics give rise to other emergent structures appearing at yet higher levels of description. Thus the molecules of chemistry emerge from nonlinear interactions between the elements of atomic physics, providing a structural basis for the proteins and ribonucleic acids of biochemistry, and so on, up through the many levels of activity in a living organism. The intricacy of this hierarchical perspective is much closer to reality, and its discovery is a watershed in the history of science. This book is intended for graduate students and researchers in physics, applied mathematics, biomathematics, biophysics and engineering. Unknown function: