Related papers: Transparent nonlinear networks
We recall the notion of (vertical) translating solitons in a product of a semi-Riemannian manifold $(M,g)$ and the real line. Mainly, we restrict our attention to those which are the graph of a smooth function. When dealing with…
We use the mathematical toolbox of the inverse scattering transform to study quantitatively the number of solitons in far from equilibrium one-dimensional systems described by the defocusing nonlinear Schr{\"o}dinger equation. We present a…
Nonlinearity in the Schr\"odinger equation gives rise to rich phenomena such as soliton formation, modulational instability, and self-organization in diverse physical systems. Motivated by recent advances in engineering nonlinear gauge…
In this article we apply quaternionic linear algebra and quaternionic linear system theory to develop the inverse scattering transform theory for the nonlinear Schr\"odinger equation with nonvanishing boundary conditions. We also determine…
This paper considers the neutron transport equation in bounded domain with a combination of the diffusive boundary condition and the in-flow boundary condition. We firstly study the existence of solution in any fixed time by…
We derive a non-linear sigma-model for the transport of light (classical waves) through a disordered medium. We compare this extension of the model with the well-established non-linear sigma-model for the transport of electrons…
In this paper, an extended nonlinear Schrodinger equation with higher-order that includes fifth-order dispersion with matching higher-order nonlinear terms is investigated under zero boundary condition at infinity. Carrying out the spectral…
Brief review of the methods for solving the multicomponent nonlinear Schrodinger (MNLS) equations and analysis of their Hamiltonian structures is given. Main attention is paid to the MNLS related to the C.II- and D.III-types symmetric…
In this manuscript, we shall investigate the Nonlinear Magnetic Schr\"odinger Equation on noncompact metric graphs, focusing on the existence of ground states. We prove that the magnetic Hamiltonian is variationally equivalent to a…
We introduce a non-exponential radiative framework that takes into account the local spatial correlation of scattering particles in a medium. Most previous works in graphics have ignored this, assuming uncorrelated media with a uniform,…
A nonlocal-in-time problem for the abstract Schr\"odinger equation is considered. By exploiting the linear nature of nonlocal condition we derive an exact representation of the solution operator under assumptions that the spectrum of…
A spectral mapping theorem is proved that resolves a key problem in applying invariant manifold theorems to nonlinear Schr\" odinger type equations. The theorem is applied to the operator that arises as the linearization of the equation…
In this paper we consider the Schr\"odinger equation on a network formed by a tree with the last generation of edges formed by infinite strips. We give an explicit description of the solution of the linear Schr\"odinger equation with…
We introduce a nonlinear operator to model diffusion on a complex undirected network under crowded conditions. We show that the asymptotic distribution of diffusing agents is a nonlinear function of the nodes' degree and saturates to a…
We consider the Schr\"odinger equation with a (matrix) Hamiltonian given by a second order difference operator with nonconstant growing coefficients, on the half one dimensional lattice. This operator appeared first naturally in the…
We present four examples of integrable partial differential equations (PDEs) of mathematical physics that---when linearized around a stationary soliton---exhibit scattering without reflection at {\it all} energies. Starting from the most…
Network models, which abstractly are given by lax symmetric monoidal functors, are used to construct operads for modeling and designing complex networks. Many common types of networks can be modeled with simple graphs with edges weighted by…
In this communication we report on a peculiar property of barrier transmission that systems governed by the nonlinear Schroedinger equation share with the linear one: For unit transmission the potential can be divided at an arbitrary point…
We consider an explicitly solvable model (formulated in the Riemannian geometry terms) for a stationary wave process in a specific thin domain with the Dirichlet boundary conditions on the boundary of the domain. The transition from the…
The analysis of datasets taking the form of simple, undirected graphs continues to gain in importance across a variety of disciplines. Two choices of null model, the logistic-linear model and the implicit log-linear model, have come into…