Redes Sociais


Colóquios 2014


Nonlinear Waves in Physics - from tsunami and freak waves to optical signal transport
Anfiteatro Antônio Cabral - Porto Alegre
Colóquios 2014


Nonlinear Waves in Physics - from tsunami and freak waves to optical signal transport

Ioannis Kourakis

Nature is intrinsically nonlinear! This means that the dynamic response of a
physical system to an external stimulus is not proportional to its strength, as often
thought, but may manifest a rich, multifaceted and often unpredictable qualitative
behaviour. The associated modelling (description of dynamics) is dominated by
nonlinear mathematical laws. Nonlinear dynamics are nowadays recognized as an
ubiquitous inherent characteristic of Nature, dominating evolution not only in science,
but also in economy, in sociology and in psychology, to mention but a few [1].

Qualitatively speaking, various physical mechanisms are generic, in that they
are present in different physical contexts. Small excitations off equilibrium, in the
presence of a restoring mechanism, are known to lead to propagating oscillations
around the equilibrium state (waves). Beyond the small-wave-amplitude
approximation, nonlinearity may become the dominant effect, leading to wave
steepening and eventually wave breakdown (surfer’s wave effect). Fourier
dispersion, on the other hand, leads to separation among different modes and
wavepacket dissociation (a phenomenon analogous to chromatic dispersion in linear
optics, the mechanism underlying the rainbow effect). When physical circumstances
allow a balance between these two mechanisms, propagating localized structures
are formed, in the form of solitary waves (modelled via the mathematical paradigm of
a soliton). Localized modes described this way may vary in form and bear various
names in different branches of physics, including solitary pulses, kink solitons,
shocks, propagating fronts, blast waves, envelope waves, rogue (freak waves),
oscillons, and so on [2-4].

An overview of the qualitative aspects leading to the formation of nonlinear
waves are in various physical contexts will be presented. Topics will range from
ocean dynamics to signal transmission in DNA strands, and from laser-plasma
interactions to pulse transmission along optical fibers. We will discuss the
mechanisms involved in the formation and propagation of solitary waves, and their
manifestation in the real world. Focus will be made to the unifying aspects linking the
mathematical description of nonlinear phenomena across different disciplines.

[1] A.C. Scott, The nonlinear universe: chaos, emergence, life (2007, Springer, Berlin)
[2] A.C. Scott, F.Y.F. Chu and D.W. McLaughlin, The Soliton: A New Concept in Applied
Science, Proc. IEEE, Vol. 61 (10), 1443 (1973)
[3] Dynamical characteristics of solitary waves, shocks and envelope modes in kappa-
distributed non-thermal plasmas: an overview, I. Kourakis, S. Sultana and M.A. Hellberg,
Plasma Phys. Cont. Fusion, 54, 124001 (2012).
[4] Freak waves and electrostatic wavepacket modulation in a quantum electron-positron-ion
plasma, M. McKerr, I. Kourakis, F. Haas, Plasma Phys. Cont. Fusion 56, 035007 (2014).


Anfiteatro Antônio Cabral
Porto Alegre
Rio Grande do Sul
País: br


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Sexta, Dezembro 03, 2021