Higher-order Spectral Filtering Effects on the Evolution of Stationary Dissipative Solitons

A semianalytical method to study the effects of the higher-order spectral filtering in the cubic-quintic complex Swift-Hohenberg equation (CSHE) through the dynamics of one soliton was applied. The approach is based on a reduction from an infinite-dimensional dynamical dissipative system to a finite-dimensional model. This formulation is helpful to study the ground state of the soliton dynamic since it depends on a trial function and a good set of parameters. With real coefficients, the CSHE exhibits stationary dissipative solitons in space with the equation parameters, and the higher-order spectral filtering has a real impact on the cartographies of stationary soliton domain. The detailed analysis reveals the effects of spectral filtering term on the stationary soliton parameters, and displays that it differently influences the cubic and quintic terms of the CSHE. The results highlight the major influence of the spectral filtering on the temporal width of the stationary soliton whereas it does not have a real impact on the amplitude and the spatial width.

THERMAL SOLITONS AND SOLECTRONS IN 1D ANHARMONIC LATTICES UP TO PHYSIOLOGICAL TEMPERATURES

We study the thermal excitation of solitons in 1D Toda–Morse lattices in a wide range of temperatures from zero up to physiological level (about 300 K) and their influence on added excess electrons moving on the lattice. The lattice units are treated by classical Langevin equations. The electron distributions are in a first estimate represented by equilibrium adiabatic distributions in the actual fields. Further, the electron dynamics is modeled in the framework of the tight-binding approximation including on-site energy shifts due to electron-lattice coupling and stochastic hopping between the sites. We calculate the electron distributions and discuss the excitations of solectron type (electron-soliton dynamic bound states) and estimate their life times.