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 waveguides. 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, in turn, needs certain simplifications in order to grasp the
physical phenomena involved. What makes this book special compared
to other books in the field is that all the examples are cast into
a general philosophical network of complexity and simplicity.
Audience: This volume will be of interest to researchers and
students whose work involves mathematical modelling of wave
phenomena.
