The BK System: Soliton Dynamics in media with Wave Field Stochastic Fluctuations (theory and applications)

The soliton dynamics in complex continuous media with the
wave field’s stochastic fluctuations which is described by the
generalized equations of the Belashov-Karpman (BK) system
including the Kadomtsev-Petviashvili (GKP) and the nonlinear
Schrodinger (GNLS) classes of equations is studied analytically
and numerically. In our investigations we take into account
the generalizations relevant to various complex physical media
including space plasma, atmosphere, hydrosphere, optical fibers
and waveguides and other complex dispersive media, where the
stochastic fluctuations of wave field takes place always, on a level
with the high-order dispersion effects, influence of dissipation
and instabilities of different types. The results on influence of
Gaussian noise on structure, stability and interaction dynamics
of the multidimensional nonlinear waves and solitons, when the
waves and solitons are deformed during the propagation, acquiring
oscillating structure are presented. The analysis of stability
of solutions is based on study of transformational properties of
the Hamiltonian of the corresponding system. The structure of
possible multidimensional solutions and their collisional interaction
is studied numerically. This is consistent representation
of the both earlier known and new original results obtained by
authors and also some generalizations in theory of the nonlinear
waves and solitons in complex dispersive media with presence
of stochastic fluctuations of the wave field. Some applications of
obtained results in real physical media are presented.