Soliton complexity in the damped-driven nonlinear Schr\"odinger equation: stationary, periodic, quasiperiodic complexes

Stationary and oscillatory bound states, or complexes, of the damped-driven solitons are numerically path-followed in the parameter space. We compile a chart of the two-soliton attractors, complementing the one-soliton attractor chart.Comment: 12 pages, 7 figure

Vibration spectra of benzene-like models with Hooke's law interactions

The harmonic oscillations of a spring-ball model of benzene-like nanosystems with Hooke's law interactions between nearest, second, and third neighbors are explored. We show that in the cylindrical coordinates the dynamics of this cyclic hexagonal system is described by the Lagrange equations similar to those of the one-dimensional two-component crystal model. We expose that the vibration frequencies of the hexagonal model lie on the branches of the dispersion law of the associated lattice model, and their positions are determined by the cyclic Born-Von Karman condition. The hexagonal model is generalized to one describing the benzene molecule and the fully deuterated and halogenated benzenes. The effect of hybridization of vibration modes and the pushing apart of spectral branches in the crossover situation is revealed. All the discrete frequency spectrum and normal modes of oscillations and their explicit dependencies on all the constants of elastic interactions are exactly found.Comment: 25 pages, 10 figure

Dynamics of bound soliton states in regularized dispersive equations

The nonstationary dynamics of topological solitons (dislocations, domain walls, fluxons) and their bound states in one-dimensional systems with high dispersion are investigated. Dynamical features of a moving kink emitting radiation and breathers are studied analytically. Conditions of the breather excitation and its dynamical properties are specified. Processes of soliton complex formation are studied analytically and numerically in relation to the strength of the dispersion, soliton velocity, and distance between solitons. It is shown that moving bound soliton complexes with internal structure can be stabilized by an external force in a dissipative medium then their velocities depend in a step-like manner on a driving strength

Sine-Gordon wobbles through bäcklund transformations

In this work we construct the wobble exact solution of sine-Gordon equation by means of B acklund Transformations. We nd the parameters of the transformations corresponding to the Bianchi diagram for the wobble as a particular 3-soliton solutions. We show that this solution agrees with the wobbles obtained by K albermann and Segur by means of the Inverse Scattering Transform, and by Ferreira et al. using the Hirota method. The new formulation introduced allows to identify easily the parameters that de ne the building blocks of this solution - a kink and a breather, and can be used in further studies of this solution in the perturbed sine-Gordon equation.We acknowledge nancial support from MICINN through grants MOSAICO (SC, AS) and FIS2008-02380/FIS (NRQ), and grants FQM207 and P06-FQM-01735 (NRQ) (from Junta de Andalucía, Spain), and SIMUMAT-CM (AS) (from Comunidad de Madrid, Spain).Publicad

Soliton trains in dispersive media

In this paper two Boussinesq-type mathematical models are described which lead to solitonic solutions. One case corresponds to microstructured solids, another case to biomembranes. The emergence of soliton trains in both cases is demonstrated by using numerical simulation. The pseudospectral method guarantees the high accuracy in computing. The significance of the nonlinearities — either deformation-type or displacement-type, is demonstrated