EDITORIAL. Special issue devoted to the International Conference on Complexity of Nonlinear Waves. Highlights in the research into complexity of nonlinear waves

Abstract

We reflect highlights of studies into a variety of phenomena reflecting the complexity of underlying nonlinear processes in a selection of research disciplines in the Centre of Nonlinear Studies (CENS), presented in the International Conference on Complexity of Nonlinear Waves, 5-7 October 2009, Tallinn, Estonia. We emphasize the similarity of mathematical description of and potential synergy arising from complementary studies in general soliton science, wave propagation in microstructured and functionally graded materials, related inverse problems, issues of nondestructive testing, weak resonant interactions of water waves, wave transformation and run-up, soliton interactions in shallow water, and selected problems of passive scalar turbulence.

Complexity in engineering and natural sciences

“…-elaborating a cross-bridge model for mechanoenergetics of actomyosin interactions; -proposing an integrated method to quantify calcium fluxes in cardiac excitation-contraction coupling; -analysis of lattice-like obstructions to diffusion in heart muscle cells. Even this brief overview demonstrates clearly how useful the interdisciplinary approach is -complexity studies are characterized by interactions and similarity of methods and concepts permit more effectively to analyse various dynamical processes [18,19]. It is not only the physical processes, similar methods can be used also for the analysis of financial markets [37].…”