Related papers: Information transport by sine-Gordon solitons in m…
We give arguments for the existence of {\it exact} travelling-wave (in particular solitonic) solutions of a perturbed sine-Gordon equation on the real line or on the circle, and classify them. The perturbation of the equation consists of a…
Solitary waves propagation of baryonic density perturbations, ruled by the Korteweg--de Vries equation in a mean-field quark-gluon plasma model, are investigated from the point of view of the theory of information. A recently proposed…
We consider the ultrashort light pulse propagation through an inhomogeneous monomodal optical fiber exhibiting higher-order dispersive effects. Wave propagation is governed by a generalized nonlinear Schr\"{o}dinger equation with varying…
We (re)cosider the propagation of small disturbances (sound waves) in the presence of a pinned irrotational vortex in a superfluid with the help of the formalism of acoustic spacetimes. We give closed formulas for the scattering angle for…
We obtain the exact solution of the Klein-Gordon equation describing the propagation of a particle in two regions of different constant magnetic field, separated by an infinite plane wall. The continuity of the wave function and of its…
We consider the sine-Gordon equation on metric graphs with simple topologies and derive vertex boundary conditions from the fundamental conservation laws, such as energy and current conservation. Traveling wave solutions for star and tree…
Nonlinear wave propagation plays a crucial role in the functioning of many physical and biophysical systems. In the propagation regime, disturbances due to the presence of local external perturbations, such as localised defects or boundary…
We derive model equations for optical pulse propagation in a medium described by a two-level Hamiltonian, without the use of the slowly varying envelope approximation. Assuming that the resonance frequency of the two-level atoms is either…
With the aid of the symbolic computations software; Wolfram Mathematica 9, the powerful sine-Gordon expansion method is used in examining the analytical solution of the longitudinal wave equation in a magneto-electro-elastic circular rod.…
In this paper we argue that, in addition to electrical and chemical signals propagating in the neurons of the brain, signal propagation takes place in the form of biophoton production. This statement is supported by recent experimental…
The problem of stability and spectrum of linear excitations of a soliton (kink) of the dispersive sine-Gordon and $\varphi^4$ - equations is solved exactly. It is shown that the total spectrum consists of a discrete set of frequencies of…
In this paper the heat transport in microtubules (MT) is investigated. When the dimension of the structure is of the order of the de Broglie wave length the transport phenomena must be analyzed within quantum mechanics. In this paper we…
We derive exact solutions to the sine--Gordon equation describing localized structures on the background of librational and rotational travelling waves. In the case of librational waves, the exact solution represents a localized spike in…
The paper proposes an envelope soliton model of the electron. The soliton propagates within a waveguide which size varies with the potential. The soliton is the solution of the Schroedinger equation with the addition of a nonlinear term…
An effort was conducted to study temporal soliton pulse propagation in silicon nano-waveguides. These nonlinear phenomenas were studied both numerically and experimentally with phase-resolved Frequency Resolved Optical Gating. Soliton pulse…
The guiding and transport of energy, for example of electromagnetic waves underpins many technologies that have shaped modern society, ranging from long distance optical fibre telecommunications to on-chip optical processors. Traditionally,…
The self-consistent spatiotemporal evolution of drift wave (DW) radial envelope and zonal flow (ZF) amplitude is investigated in a slab model [1]. Stationary solution of the coupled partial differential equations in a simple limit yields…
We present in closed form some special travelling-wave solutions (on the real line or on the circle) of a perturbed sine-Gordon equation. The perturbation of the equation consists of a constant forcing term $\gamma$ and a linear dissipative…
Using the transfer matrix technique, we investigate the propagation of electron through a two dimensional disordered sample. We find that the spatial distribution of electrons is homogeneous only in the limit of weak disorder (diffusive…
Signal propagation in neuronal dendrites represents the basis for interneuron communication and information processing in the brain. Here we take into account charge inhomogeneities arising in the vicinity of ion channels in cytoplasm and…