Related papers: Transparent PT-symmetric nonlinear networks
We will discuss a one-dimensional approximation for the problem of wave propagation in networks of thin fibers. The main objective here is to describe the boundary (gluing) conditions at branching points of the limiting one-dimensional…
The existence of nonzero periodic travelling wave solutions for a general discrete nonlinear Schr\"odinger equation (DNLS) on finite one-dimensional lattices is proved. The DNLS features a general nonlinear term and variable range of…
We develop a detailed rigorous analysis of edge bifurcations of standing waves in the nonlinear Schr\"odinger (NLS) equation on a tadpole graph (a ring attached to a semi-infinite line subject to the Kirchhoff boundary conditions at the…
We explore the phenomena of absorption/emission of solitons by an integrable boundary for the nonlinear Schr\"odinger equation on the half-line. This is based on the investigation of time-dependent reflection matrices which satisfy the…
When the coefficients of the cubic terms match the coefficients in the boundary conditions at a vertex of a star graph and satisfy a certain constraint, the nonlinear Schr\"{o}dinger (NLS) equation on the star graph can be transformed to…
Graphical models have been popularly used for capturing conditional independence structure in multivariate data, which are often built upon independent and identically distributed observations, limiting their applicability to complex…
We consider non-selfadjoint operators of the kind arising in linearized NLS and prove dispersive bounds for the time-evolution without assuming that the edges of the essential spectrum are regular. Our approach does not depend on any…
In graphene, where the electron-electron scattering is dominant, electrons collectively act as a fluid. This hydrodynamic behaviour of charge carriers leads to exciting nonlinear phenomena such as solitary waves and shocks, among others. In…
Unidirectional reflectionless propagation (or transmission) is an interesting wave phenomenon observed in many $\mathcal{PT}$-symmetric optical structures. Theoretical studies on unidirectional reflectionless transmission often use simple…
Nonlinear Schr\"{o}dinger equation was originally derived in nonlinear optics as a model for beam propagation, which naturally requires its application in cylindrical coordinates. However, the derivation was done in the Cartesian…
The models of the non-linear optics in which solitons were appeared are considered. These models are of paramount importance in studies of non-linear wave phenomena. The classical examples of phenomena of this kind are the self-focusing,…
We consider the existence of normalized solutions to nonlinear Schr\"odinger equations on noncompact metric graphs in the $L^2$ supercritical regime. For sufficiently small prescribed mass ($L^2$ norm), we prove existence of positive…
In this article, we discuss the efficient ways of implementing the transparent boundary condition (TBC) and its various approximations for the free Schr\"{o}dinger equation on a hyperrectangular computational domain in $\field{R}^d$ with…
We introduce and analyze a symmetric low-regularity scheme for the nonlinear Schr\"odinger (NLS) equation beyond classical Fourier-based techniques. We show fractional convergence of the scheme in $L^2$-norm, from first up to second order,…
The nonlinear Schr\"odinger (NLS) equation and the Whitham modulation equations both describe slowly varying, locally periodic nonlinear wavetrains, albeit in differing amplitude-frequency domains. In this paper, we take advantage of the…
In this paper, we study one-dimensional linear Schr\"odinger equations with multiple moving potentials, known as transfer charge models. Focusing on the non-self-adjoint setting that arises in the study of solitons, we systematically…
We build Gaussian wave packets for the linear Schr\"odinger equation and its finite difference space semi-discretization and illustrate the lack of uniform dispersive properties of the numerical solutions as established in Ignat, Zuazua,…
We integrate the one-dimensional nonlinear Schr\"odinger equation numerically for solitons moving in external potentials. In particular, we study the scattering off an interface separating two regions of constant potential modeled by a…
Nonreciprocal transmission forms the basic operation mechanism of optical diodes and isolators and requires the tantalizing task of breaking the Lorentz reciprocity law. In this work, strong nonreciprocal transmission is demonstrated by…
The two-dimensional cubic nonlinear Schrodinger equation (NLS) can be used as a model of phenomena in physical systems ranging from waves on deep water to pulses in optical fibers. In this paper, we establish that every one-dimensional…