Nonlinear electron oscillations in a viscous and resistive plasma.

Nonlinear, spatially periodic, long-wavelength electrostatic modes of an electron fluid oscillating against a motionless ion fluid (Langmuir waves) are given, with viscous and resistive effects included. The cold plasma approximation is adopted, which requires the wavelength to be sufficiently large. The pertinent requirement valid for large amplitude waves is determined. The general nonlinear solution of the continuity and momentum transfer equations for the electron fluid along with Poisson's equation is obtained in simple parametric form. It is shown that in all typical hydrogen plasmas, the influence of plasma resistivity on the modes in question is negligible. Within the limitations of the solution found, the nonlinear time evolution of any (periodic) initial electron number density profile ne(x,t=0) can be determined (examples). For the modes in question, an idealized model of a strictly cold and collisionless plasma is shown to be applicable to any real plasma, provided that the wavelength λ>>λmin(n(0),Te) , where n(0)=const and Te are the equilibrium values of the electron number density and electron temperature. Within this idealized model, the minimum of the initial electron density n(e)(xmin,t=0) must be larger than half its equilibrium value, n(0)/2 . Otherwise, the corresponding maximum n(e)(xmax,t=τ(p)/2) , obtained after half a period of the plasma oscillation blows up. Relaxation of this restriction on n(e)(x,t=0) as one decreases λ , due to the increase of the electron viscosity effects, is examined in detail. Strong plasma viscosity is shown to change considerably the density profile during the time evolution, e.g., by splitting the largest maximum in two.

Theoretical confirmation of Feynman's hypothesis on the creation of circular vortices in Bose-Einstein condensates: III.

In two preceding papers (Infeld and Senatorski 2003 J. Phys.: Condens. Matter 15 5865, Senatorski and Infeld 2004 J. Phys.: Condens. Matter 16 6589) the authors confirmed Feynman's hypothesis on how circular vortices can be created from oppositely polarized pairs of linear vortices (first paper), and then gave examples of the creation of several different circular vortices from one linear pair (second paper). Here, in part III, we give two classes of examples of how the vortices can interact. The first confirms the intuition that the reconnection processes which join two interacting vortex lines into one, and thus increase the degree of entanglement of the vortex system, practically do not occur. The second shows that new circular vortices can also be created from pairs of oppositely polarized coaxial circular vortices. This seems to contradict the results for such pairs given in Koplik and Levine (1996 Phys. Rev. Lett. 76 4745).

Analytically solvable model of nonlinear oscillations in a cold but viscous and resistive plasma.

A method for solving model nonlinear equations describing plasma oscillations in the presence of viscosity and resistivity is given. By first going to the Lagrangian variables and then transforming the space variable conveniently, the solution in parametric form is obtained. It involves simple elementary functions. Our solution includes all known exact solutions for an ideal cold plasma and a large class of new ones for a more realistic plasma. A new nonlinear effect is found of splitting of the largest density maximum, with a saddle point between the peaks so obtained. The method may sometimes be useful where inverse scattering fails.

Statics and dynamics of Bose-Einstein condensates in double square well potentials.

We treat the behavior of Bose-Einstein condensates in double square well potentials of both equal and different depths. For even depth, symmetry preserving solutions to the relevant nonlinear Schrödinger equation are known, just as in the linear limit. When the nonlinearity is strong enough, symmetry breaking solutions also exist, side by side with the symmetric one. Interestingly, solutions almost entirely localized in one of the wells are known as an extreme case. Here we outline a method for obtaining all these solutions for repulsive interactions. The bifurcation point at which, for critical nonlinearity, the asymmetric solutions branch off from the symmetry preserving ones is found analytically. We also find this bifurcation point and treat the solutions generally via a Josephson junction model. When the confining potential is in the form of two wells of different depth, interesting phenomena appear. This is true of both the occurrence of the bifurcation point for the static solutions and also of the dynamics of phase and amplitude varying solutions. Again a generalization of the Josephson model proves useful. The stability of solutions is treated briefly.

Fully three dimensional breather solitons can be created using feshbach resonances.

We investigate the stability properties of breather solitons in a three-dimensional Bose-Einstein condensate with Feshbach resonance management of the scattering length and confined only by a one-dimensional optical lattice. We compare regions of stability in parameter space obtained from a fully 3D analysis with those from a quasi-two-dimensional treatment. For moderate confinement we discover a new island of stability in the 3D case, not present in the quasi-2D treatment. Stable solutions from this region have non-trivial dynamics in the lattice direction; hence, they describe fully 3D breather solitons. We demonstrate these solutions in direct numerical simulations and outline a possible way of creating robust 3D solitons in experiments in a Bose-Einstein condensate in a one-dimensional lattice. We point out other possible applications.

Two-dimensional dispersion-managed light bullets in Kerr media.

We propose a scheme for stabilizing spatiotemporal solitons (STSs) in media with cubic self-focusing nonlinearity and "dispersion management," i.e., a layered structure inducing periodically alternating normal and anomalous group-velocity dispersion. We develop a variational approximation for the STS, and verify results by direct simulations. A stability region for the two-dimensional (2D) STS (corresponding to a planar waveguide) is identified. At the borders between this region and that of decay of the solitons, a more sophisticated stable object, in the form of a periodically oscillating bound state of two subpulses, is also found. In the 3D case (bulk medium), all the spatiotemporal pulses spread out or collapse.