At the end of the twentieth century, nonlinear dynamics turned out to be
one of the most challenging and stimulating ideas. Notions like
bifurcations, attractors, chaos, fractals, etc. have proved to be useful
in explaining the world around us, be it natural or artificial. However,
much of our everyday understanding is still based on linearity, i. e. on
the additivity and the proportionality. The larger the excitation, the
larger the response-this seems to be carved in a stone tablet. The real
world is not always reacting this way and the additivity is simply lost.
The most convenient way to describe such a phenomenon is to use a
mathematical term-nonlinearity. The importance of this notion, i. e. the
importance of being nonlinear is nowadays more and more accepted not
only by the scientific community but also globally. The recent success
of nonlinear dynamics is heavily biased towards temporal
characterization widely using nonlinear ordinary differential equations.
Nonlinear spatio-temporal processes, i. e. nonlinear waves are seemingly
much more complicated because they are described by nonlinear partial
differential equations. The richness of the world may lead in this case
to coherent structures like solitons, kinks, breathers, etc. which have
been studied in detail. Their chaotic counterparts, however, are not so
explicitly analysed yet. The wavebearing physical systems cover a wide
range of phenomena involving physics, solid mechanics, hydrodynamics,
biological structures, chemistry, etc.
