Related papers: Shadowing of non-transversal heteroclinic chains

We examine a recently-proposed family of nonlinear Schr\"odinger equations [J. Phys. A: Math. Gen. 27:1771(1994)] with respect to a group of transformations that linearize a subfamily of them. We investigate the structure of the whole…

It is demonstrated that nonlinear dynamical systems with analytic nonlinearities can be brought down to the abstract Schr\"odinger equation in Hilbert space with boson Hamiltonian. The Fourier coefficients of the expansion of solutions to…

We derive an effective equation for the dynamics of many identical bosons in dimension one in the presence of a tiny impurity. The interaction between every pair of bosons is mediated by the impurity through a positive three-body potential.…

Let $\mathbb T$ be the differential field of transseries. We establish some basic properties of the dimension of a definable subset of ${\mathbb T}^n$, also in relation to its codimension in the ambient space ${\mathbb T}^n$. The case of…

We consider the problem of shadowing for differential equations with grow-up. We introduce so-called nonuniform shadowing properties (in which size of the error depends on the point of the phase space) and prove for them analogs of…

We introduce a new dynamical system model called the shadowing problem, where a shadower chases after an escaper by always staring at and keeping the distance from him. When the escaper runs along a planar closed curve, we associate to the…

Linear projection schemes like Proper Orthogonal Decomposition can efficiently reduce the dimensions of dynamical systems but are naturally limited, e.g., for convection-dominated problems. Nonlinear approaches have shown to outperform…

3D reconstruction is a fundamental problem in computer vision, and the task is especially challenging when the object to reconstruct is partially or fully occluded. We introduce a method that uses the shadows cast by an unobserved object in…

We present a systematic formulation of scattering theory for nonlinear interactions in one dimension and develop a nonlinear generalization of the transfer matrix that has a composition property similar to its linear analog's. We offer…

We use an adiabatic approximation in terms of instantaneous resonances to study the steady-state and time-dependent transport properties of interacting electrons in biased resonant tunneling heterostructures. This approach leads, in a…

In this paper, we consider the scattering problem for a class of $N$-coupled systems of the cubic nonlinear Schr\"odinger equations in three space dimensions. We prove the scattering of solutions that have a mass-energy quantity less than…

In this work, we introduce a family of rotating black bounces with an anisotropic fluid obtained by using a modified Newman-Janis algorithm. We analyze the main features of these spacetimes and obtain the geodesics for photons, which admit…

We describe a numerical model for the interaction of light with large raindrops using realistic nonspherical drop shapes. We apply geometrical optics and a Monte Carlo technique to perform ray traces through the drops. We solve the problem…

We consider the reflectionless transport of solitons in networks. The system is modeled in terms of the nonlinear Schr\"odinger equation on metric graphs, for which transparent boundary conditions at the branching points are imposed. This…

We consider holographic cosmological models of dark energy in which the infrared cutoff is set by the Hubble's radius. We show that any interacting dark energy model with a matter like term able to alleviate the coincidence problem (i.e.,…

In this paper, the dynamical attractor and heteroclinic orbit have been employed to make the late-time behaviors of the model insensitive to the initial condition and thus alleviate the fine-tuning problem in the torsion cosmology. The…

The phenomenon of shadowing of nuclear structure functions at small values of Bjorken-$x$ is analyzed. First, multiple scattering is discussed as the underlying physical mechanism. In this context three different but related approaches are…

In this paper a nonlinear coupled Schrodinger system in the presence of mixed cubic and superlinear power laws is considered. A non standard numerical method is developed to approximate the solutions in higher dimensional case. The idea…

An approach to find a weak form of shadowing is developed. We consider homeomorphisms of a compact metric space. It is proved that every pseudotrajectory with sufficiently small errors contains at least one subsequence that can be shadowed…

For topological dynamical systems defined by continuous self-maps of compact metric spaces, we consider the contractive shadowing property, i.e., the Lipschitz shadowing property such that the Lipschitz constant is less than 1. We prove…