Fast-slow wave transitions induced by a random mean flow.

Motivated by recent asymptotic results in atmosphere-ocean fluid dynamics, we present an idealized numerical and theoretical study of two-dimensional dispersive waves propagating through a small-amplitude random mean flow. The objective is to delineate clearly the conditions under which the cumulative Doppler shifting and refraction by the mean flow can change the group velocity of the waves not only in direction, but also in magnitude. The latter effect enables a possible transition from fast to slow waves, which behave very differently.

Direct Verification of the Kinetic Description of Wave Turbulence for Finite-Size Systems Dominated by Interactions among Groups of Six Waves.

The present work considers systems whose dynamics are governed by the nonlinear interactions among groups of 6 nonlinear waves, such as those described by the unforced quintic nonlinear Schrödinger equation. Specific parameter regimes in which ensemble-averaged dynamics of such systems with finite size are accurately described by a wave kinetic equation, as used in wave turbulence theory, are theoretically predicted. In addition, the underlying reasons that the wave kinetic equation may be a poor predictor of wave dynamics outside these regimes are also discussed.

Soliton dynamics in planar ferromagnets and anti-ferromagnets.

The aim of this paper is to present a rigorous mathematical proof of the dynamical laws for the topological solitons(magnetic vortices) in ferromagnets and anti-ferromagnets. It is achieved through the conservation laws for the topological vorticity and the weak convergence methods.