Number: MECH 159/96
Author(s): ENGELBRECHT, J.
Title: Nonlinear wave dynamics: Complexity and simplicity. 8 p.
Language: English
Keywords: nonlinearity * wave motion * modelling * complexity * evolution
equations
ABSTRACT. The general idea advocated in this book is to start from
complicated mathematical models describing wave motion as it results
from the rules of continuum mechanics and then to find a simpler viewpoint
that still keeps everything essential preserved. Special attention is
paid to the description of the sources of nonlinearities. The complexities
in modelling are demonstrated by several examples including solitons,
propagating instabilities and waves in wavequides. The selected case
studies show some unconventional approaches in order to explain the
richness of nonlinear wave motion. The final chapters are of more general
character including the essays on nonlinearity, beauty, and complexity.
In this way, the thread of the analysis is the following: simple basic
arguments result in a complicated theory that needs again certain
simplifications in order to grasp the physical phenomena involved. That
makes this book special as compared to other books in the field - all
the examples are cast into a general philosophical network of complexity
and simplicity. The book is meant for researchers and students interested
in mathematical modelling of wave phenomena.
This Research Report includes the contents and preface of the book under
the same title that has been written in 1996 according to the agreement
with Kluwer Academic Publishers, Dordrecht, The Netherlands.