We report the results of an experiment and numerical simulations that demonstrate the large spatial extent and the effect of the so-called energy reservoir during the filamentation of femtosecond laser pulses in air. By inserting pinholes of different sizes in the filament path we observe different stages of development ranging from the termination of the filament, through its partial survival, to undisturbed propagation. A background containing up to 50% of the pulse energy is found to be necessary to maintain the filament formation, including a first refocusing.

We study the nonequilibrium diffusion dynamics of supersonic lattice solitons in a classical chain of atoms with nearest-neighbor interactions coupled to a heat bath. As a specific example we choose an interaction with cubic anharmonicity. The coupling between the system and a thermal bath with a given temperature is made by adding noise, delta correlated in time and space, and damping to the set of discrete equations of motion. Working in the continuum limit and changing to the sound velocity frame we derive a Korteweg-de Vries equation with noise and damping. We apply a collective coordinate approach which yields two stochastic ODEs which are solved approximately by a perturbation analysis. This finally yields analytical expressions for the variances of the soliton position and velocity. We perform Langevin dynamics simulations for the original discrete system which confirm the predictions of our analytical calculations, namely, noise-induced superdiffusive behavior which scales with the temperature and depends strongly on the initial soliton velocity. A normal diffusion behavior is observed for solitons with very low energy, where the noise-induced phonons also make a significant contribution to the soliton diffusion.

We theoretically investigate the motion of collective excitations in the two-dimensional nonlinear Schrödinger equation with cubic nonlinearity. The form of these excitations for a broad range of parameters is derived. Their evolution and interaction is numerically studied and the modulation instability is discussed. The case of saturable nonlinearity is revisited.

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We discuss the effect of small perturbation on nodeless solutions of the nonlinear Schrödinger equation in 1+1 dimensions in an external complex potential derivable from a parity-time symmetric superpotential that was considered earlier [Phys. Rev. E 92, 042901 (2015)]. In particular we consider the nonlinear partial differential equationHere we study the perturbations as a function of b and m using a variational approximation based on a dissipation functional formalism. We compare the result of this variational approach with direct numerical simulation of the equations. We find that the variational approximation works quite well at small and moderate values of the parameter bm which controls the strength of the imaginary part of the potential. We also show that the dissipation functional formalism is equivalent to the generalized traveling wave method for this type of dissipation.