Related papers: Transparent nonlinear networks
We introduce a general model which augments the one-dimensional nonlinear Schr\"{o}dinger (NLS) equation by nonlinear-diffraction terms competing with the linear diffraction. The new terms contain two irreducible parameters and admit a…
A nonlinear Schr\"odinger equation with repulsive (defocusing) nonlinearity is considered. As an example, a system with a spatially varying coefficient of the nonlinear term is studied. The nonlinearity is chosen to be repelling except on a…
We study a current transport through a system of a few grains connected with tunneling links. The exact solution is given for an arbitrarily connected double-grain system with a shared gate in the framework of the orthodox model. The…
We consider the cubic nonlinear Schr\"{o}dinger equation on the star graph with the Kirchhoff boundary condition. We prove modified scattering for the final state problem and the initial value problem. Moreover, we also consider the failure…
We prove the existence of ground state in a multidimensional nonlinear Schrodinger model of paraxial beam propagation in isotropic local media with saturable nonlinearity. Such ground states exist in the form of bright counterpropagating…
Routing information through networks is a universal phenomenon in both natural and manmade complex systems. When each node has full knowledge of the global network connectivity, finding short communication paths is merely a matter of…
Linear theory for phonon scattering by discrete breathers in the discrete nonlinear Schroedinger equation using the transfer matrix approach is presented. Transmission and reflection coefficients are obtained as a function of the wave…
Under investigation in this work is an extended nonlinear Schr\"{o}dinger equation with nonzero boundary conditions, which can model the propagation of waves in dispersive media. Firstly, a matrix Riemann-Hilbert problem for the equation…
We introduce an exactly integrable nonlinear model describing the dynamics of spinor solitons in space-dependent matrix gauge potentials of rather general types. The model is shown to be gauge equivalent to the integrable system of vector…
We consider the linear vector Schr\"odinger equation subjected to quadratic constraints. We demonstrate that the resulting nonlinear system is closely related to the Ablowitz-Ladik hierarchy and use this fact to derive the N-soliton…
The nonlinear Schrodinger equation supports solitons -- self-interacting, localized states that behave as nearly independent objects. We exhibit solitons with self-induced nonreciprocal dynamics in a discrete nonlinear Schrodinger equation.…
We present a first principle derivation of the coupled nonlinear Schr\"{o}dinger equations that govern the interaction between two families of modes with different transverse profiles in a generic whispering-gallery-mode resonator. We find…
Mesoscopic systems and large molecules are often modeled by graphs of one-dimensional wires, connected at vertices. In this paper we discuss the solutions of the Schr\"odinger equation on such graphs, which have been named "quantum…
Conservation laws and balance equations for physical network systems typically can be described with the aid of the incidence matrix of a directed graph, and an associated symmetric Laplacian matrix. Some basic examples are discussed, and…
In this paper we study existence and uniqueness of solutions for a very general class of doubly nonlinear diffusion equations on metric graphs, which provide the appropriate mathematical framework to describe complex tubular networks in…
We consider dynamics of charged solitons in branched conducting polymers. An effective model based on the sine-Gordon equation on metric graphs is used for computing the charge transport and scattering of charge carriers at the polymer…
We analyze theoretically the Schrodinger-Poisson equation in two transverse dimensions in the presence of a Kerr term. The model describes the nonlinear propagation of optical beams in thermooptical media and can be regarded as an analogue…
The hallmark feature of topological insulators renders edge transport virtually impervious to scattering at defects and lattice disorder. In our work, we experimentally demonstrate a topological system, using a photonic platform, in which…
The existence of compactons in the discrete nonlinear Schr\"odinger equation in the presence of fast periodic time modulations of the nonlinearity is demonstrated. In the averaged DNLS equation the resulting effective inter-well tunneling…
We discuss the potential scattering on the noncompact star graph. The Schr\"{o}dinger operator with the short-range potential localizing in a neighborhood of the graph vertex is considered. We study the asymptotic behavior the corresponding…