Many extended physical systems are modelled by classical soliton
equations (KdV, SG, NLS etc.), possessing, far from equilibrium, a
variety of nontrivial solutions. The question of reaching and
controlling a particular stable solution (excitation) in this solutions
set is fundamental to many applications. One way of forming desired
solutions is based on choosing proper, frequently nontrivial
initial/boundary conditions. I will describe a different recent approach
to formation of multiplicity of nonlinear excitations from trivial
initial/boundary conditions based on capturing the system into resonance
with external perturbations followed by a continuing
self-synchronization (autoresonance) in space and/or time. The
synchronization means excursion in system’s solutions space with
possible emergence of a desired nontrivial state. Applications of this
paradigm exist in vorticity dominated flows [1], plasmas [2], as well as
in planetary dynamics [3], and molecular physics [4]. I will present
main ideas of wave autoresonance and focus on autoresonant wave
interactions in plasmas and new developments on formation and control of
large amplitude multi-phase nonlinear waves.
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