A statistical approach of the propagation of solitons in media with spatially random dispersive perturbations is developed. Applying the inverse scattering transform several regimes are put into evidence which are determined by the mass and the velocity of the incoming soliton and also by the correlation length of the perturbation. Namely, the mass of the soliton is almost conserved if it is in...

A statistical approach of the propagation of solitons in media with spatially random dispersive perturbations is developed. Applying the inverse scattering transform several regimes are put into evidence which are determined by the mass and the velocity of the incoming soliton and also by the correlation length of the perturbation. Namely, the mass of the soliton is almost conserved if it is in...

We consider thermodynamic and transport properties of a long granular array with strongly connected grains (intergrain conductance g>>1). We find that the system's conductance and differential capacitance exhibits activated behavior, approximately exp([-T(*)/T]. The gap T(*) represents the energy needed to create a long single-electron charge soliton propagating through the array. This scale is...

A world-sheet sigma model approach is applied to string theories dual to fourdimensional gauge theories, and semi-classical soliton solutions representing highly excited string states are identified which correspond to gauge theory operators with relatively small anomalous dimensions. The simplest class of such states are strings on the leading Regge trajectory, with large spin in AdS5. These c...

Stable embedded solitons are discovered in the generalized third-order nonlinear Schrödinger equation. When this equation can be reduced to a perturbed complex modified Korteweg-de Vries equation, we developed a soliton perturbation theory which shows that a continuous family of sech-shaped embedded solitons exist and are nonlinearly stable. These analytical results are confirmed by our numeric...

String theory is defined perturbatively through a set of rules for calculating scattering amplitudes. Perhaps the most important outstanding problem is that of finding the non-perturbative theory whose perturbation theory reproduces that of string theory. This seems a daunting task, but recent progress has led to some striking conjectures regarding the non-perturbative structure of the theory t...

We analyze the phase diagram of quantum chromodynamics at low-to-moderate temperature, baryon chemical potential and external magnetic field within chiral perturbation theory next-to-leading order derivative expansion. Our main result is that anomaly-induced soliton lattice (CSL) stabilized by thermal fluctuations. As a consequence, CSL state may survive up to temperatures which symmetry restor...

The behavior of linear and nonlinear dust acoustic waves (DAWs) in an unmagnetized plasma including inertialess electrons and positrons, ions, and mobile positive/negative dust grains are studied. Reductive perturbation method is employed for small and finite amplitude DAWs. To investigate the solitary waves, the Korteweg–de Vries (KdV) equation is derived and the solution is presented. B...