Structure and evolution of magnetohydrodynamic solitary waves with Hall and finite Larmor radius effects.

Nonlinear and low-frequency solitary waves are investigated in the framework of the one-dimensional Hall-magnetohydrodynamic model with finite Larmor effects and two different closure models for the pressures. For a double adiabatic pressure model, the organization of these localized structures in terms of the propagation angle with respect to the ambient magnetic field θ and the propagation velocity C is discussed. There are three types of regions in the θ-C plane that correspond to domains where either solitary waves cannot exist, are organized in branches, or have a continuous spectrum. A numerical method valid for the two latter cases, which rigorously proves the existence of the waves, is presented and used to locate many waves, including bright and dark structures. Some of them belong to parametric domains where solitary waves were not found in previous works. The stability of the structures has been investigated by performing a linear analysis of the background plasma state and by means of numerical simulations. They show that the cores of some waves can be robust, but, for the parameters considered in the analysis, the tails are unstable. The substitution of the double adiabatic model by evolution equations for the plasma pressures appears to suppress the instability in some cases and to allow the propagation of the solitary waves during long times.

Quasicollapse of oblique solitons of the weakly dissipative derivative nonlinear Schrödinger equation.

Numerical integrations of the derivative nonlinear Schrödinger equation for Alfvén waves, supplemented by a weak dissipative term (originating from diffusion or Landau damping), with initial conditions in the form of a bright soliton with nonvanishing conditions at infinity (oblique soliton), reveal an interesting phenomenon of "quasicollapse": as the dissipation parameter is reduced, larger amplitudes are reached and smaller scales are created, but on an increasing time scale. This process involves an early bifurcation of the initial soliton toward a breather that is analyzed by means of a numerical inverse scattering technique. This evolution leads to the formation of persistent dark solitons that are only weakly affected when crossed by the decaying breather which has the form of either a localized structure or an extended wave packet.

Effect of a random noise on scaling laws of finite Prandtl number rotating convection near threshold.

A generalized Swift-Hohenberg model including a weak random forcing, viewed as mimicking the intrinsic source of noise due to boundary defects, is used to reproduce the experimentally observed power-law variation of the correlation length of rotating convection patterns as a function of the stress parameter near threshold, and to demonstrate the sensitivity of the exponent to the amplitude of the superimposed random noise. The scaling properties of rotating convection near threshold are thus conjectured to be nonuniversal.