The possibility of unidirectional motion of a kink (topological soliton) of a dissipative sine-Gordon equation in the presence of ac forces with harmonic mixing (at least biharmonic) and of zero mean, is presented. The dependence of the kink mean velocity on system parameters is investigated numerically and the results are compared with a perturbation analysis based on a point-particle represen...

A new integrable (2+1)-dimensional nonlocal nonlinear Schrödinger equation is proposed. The N-soliton solution is given by Gram type determinant. It is found that the localized N-soliton solution has interesting interaction behavior which shows change of amplitude of localized pulses after collisions .

We re-examine three issues, the Hopf term, fractional spin and the soliton operators, in the 2 + 1 dimensional O(3) nonlinear sigma model based on the adjoint orbit parametrization (AOP) introduced earlier. It is shown that the Hopf term is well-defined for configurations of any soliton charge Q if we adopt a time independent boundary condition at spatial infinity. We then develop the Hamiltoni...

A protean topological soliton has recently been shown to emerge in systems of repulsive particles in cylindrical geometries, whose statics is described by the number-theoretical objects of phyllotaxis. Here, we present a minimal and local continuum model that can explain many of the features of the phyllotactic soliton, such as locked speed, screw shift, energy transport, and--for Wigner crysta...

A dispersion-managed optical system with stepwise periodic variation of dispersion is studied in the framework of a path-averaged Gabitov-Turitsyn equation. The soliton solution is obtained by means of iterating the path-averaged equation. The dependence of soliton parameters on dispersion map strength is investigated, together with the oscillating tails of the soliton.

Stochastic dynamics o f a soliton in a long optical fiber is analysed within the framework of the nonlinear Schr6dinger equation. It is shown that in the case of periodic perturbations describing, e.g. sound propagation along a fiber, adiabatic dynamics of a soliton may be stochastic, and the condition for this stochastic motion is obtained. In the case of random perturbations we obtain the sol...

The scale invariance of the O(3) sigma model can be broken by gauging a U(1) subgroup of the O(3) symmetry and including a Maxwell term for the gauge field in the Lagrangian. Adding also a suitable potential one obtains a field theory of Bogomol’nyi type with topological solitons. These solitons are stable against rescaling and carry magnetic flux which can take arbitrary values in some finite ...

It is shown that a gauged nonlinear O(3) sigma model with anomalous magnetic moment interaction in 2 + 1 dimensions is exactly integrable for static, self-dual field configurations. The matter fields are exactly equivalent to those of the usual ungauged nonlinear O(3) sigma model. These static soliton solutions can be mapped into an Abelian purely magnetic vortex solutions through a suitable re...

We investigate a 2-dimensional N = 2 supersymmetric model which consists of n chiral superfields with Kähler potential. When we define quantum observables, we are always plagued by operator ordering problem. Among various ways to fix the operator order, we rely upon the supersymmetry. We demonstrate that the correct operator order is given by requiring the super Poincaré algebra by carrying out...

We propose a mechanism for fixing the velocity of relativistic soliton based on the breaking of the Lorentz symmetry of the sine-Gordon (SG) model. The proposal is first elaborated for a molecular chain model, as the simple pendulum limit of a double pendulums chain. It is then generalized to a full class of two-dimensional field theories of the sine-Gordon type. From a phenomenological point o...