We consider the continuum version of an elastic chain supporting topological and non-topological degrees of freedom; this generalizes a model for the dynamics of DNA recently proposed and investigated by ourselves. In a certain limit, the non-topological degrees of freedom are frozen, and the model reduces to the sine-Gordon equations and thus supports well-known topological soliton solutions. ...

A procedure allowing for the construction of Lorentz invariant integrable models living in d+1 dimensional space-time and with an n dimensional target space is provided. Here, integrability is understood as the existence of the generalized zero-curvature formulation and infinitely many conserved quantities. A close relation between the Lagrange density of the integrable models and the pullback ...

The O(3) nonlinear sigma model with boundary, in dimension two, is considered. An algorithm to determine all its soliton solutions that preserve a rotational symmetry in the boundary is exhibited. This nonlinear problem is reduced to that of clamped elastica in a hyperbolic plane. These solutions carry topological charges that can be holographically determined from the boundary conditions. As a...

We propose solitons in a photonic topological insulator: self-localized wave packets forming topological edge states residing in the bulk of a nonlinear photonic topological insulator. These self-forming entities exhibit, despite being in the bulk, the property of unidirectional transport, similar to the transport their linear counterparts display on the edge of a topological insulator. In the ...

The O(3) nonlinear sigma model with boundary, in dimension two, is considered. An algorithm to determine all its soliton solutions that preserve a rotational symmetry in the boundary is exhibited. This nonlinear problem is reduced to that of clamped elastica in a hyperbolic plane. These solutions carry topological charges that can be holographically determined from the boundary conditions. As a...

We consider two exit problems for the Korteweg-de Vries equation perturbed by an additive white in time and colored in space noise of amplitude ǫ. The initial datum gives rise to a soliton when ǫ = 0. It has been proved recently that the solution remains in a neighborhood of a randomly modulated soliton for times at least of the order of ǫ. We prove exponential upper and lower bounds for the sm...

In ultrafast optics, optical pulses are generated to be of shorter pulse duration, which has enormous significance to industrial applications and scientific research. The ultrashort pulse evolution in fiber lasers can be described by the higher-order Ginzburg-Landau (GL) equation. However, analytic soliton solutions for this equation have not been obtained by use of existing methods. In this pa...

We consider two exit problems for the Korteweg-de Vries equation perturbed by an additive white in time and colored in space noise of amplitude . The initial datum gives rise to a soliton when = 0. It has been proved recently that the solution remains in a neighborhood of a randomly modulated soliton for times at least of the order of −2. We prove exponential upper and lower bounds for the smal...

In this paper, a general bright-dark soliton solution in the form of Pfaffian is constructed for an integrable semi-discrete vector NLS equation via Hirota’s bilinear method. Oneand two-bright-dark soliton solutions are explicitly presented for two-component semidiscrete NLS equation; two-bright-one-dark, and one-bright-two-dark soliton solutions are also given explicitly for three-component se...

Sine-Gordon (SG) models with variable mass or perturbed soliton appear in many physical situations, which however breaks the integrability of the model. A class of such inhomogeneous models with accelerating and shape changing solitons is constructed, which are integrable both at the classical and the quantum level with exact solutions. PACS: 05.45.Yv,03.65.Fd,11.10.Lm,11.55.Ds Among the exclus...