The basic theme of modern nonlinear science is the interplay between chaos and coherent structures. Formerly deemed unworthy of the attention of a serious scientist, low order systems of nonlinear ordinary differential equations are now known to exhibit explosive behavior, leading to the emergence of strange attractors upon which phase space trajectories wander aimlessly until the end of time. Largely ignored as being far too difficult to solve analytically, nonlinear partial differential equations have been found to generate the emergence of solitary waves, which interact as new dynamic entities at higher levels of description.
These new paradigms are far more significant than the mere reformulation of old knowledge into different patterns. Again and again, the theoretical perspectives of modern nonlinear science have suggested research leading to significant advances in understanding. Studies in chaotic dynamics, for example, have explained the puzzling "excess noise" in (superconducting) Josephson mixers and oscillators, increased our understanding of wheel wear on high speed railways, and provided new insights into the functioning of biological control systems. The emergent entities of solitary wave theory include information carrying pulses on optical fibers, nerve axons, and superconducting transmission lines; local modes on small molecules and molecular crystals; in addition to the better known hydrodynamic examples of bores and vortices.
As evidence of the importance and intellectual vigor of these developments, one can point to several successful new journals (PHYSICA D, PHYSICAL REVIEW E, NONLINEARITY, among others) and the many interdisciplinary, international conferences and workshops in the area.
It is in the spirit of this growing activity that our work is conducted. Although seemingly diverse at first reading, the facets of our research are, in fact, closely interrelated components of modern research in nonlinear dynamics including scientific computing and experimental research.
Back to home.