Related papers: Simulating DNLS models
We describe computational tools that have been developed to simulate dynamical mass transfer in semi-detached, polytropic binaries that are initially executing synchronous rotation upon circular orbits. Initial equilibrium models are…
The Dyson Brownian Motion (DBM) describes the stochastic evolution of $N$ points on the line driven by an applied potential, a Coulombic repulsion and identical, independent Brownian forcing at each point. We use an explicit tamed Euler…
As a complementary tool to laboratory experiments, discrete numerical simulation, applied to granular materials, provides valuable information on the grain and contact scale microstructure, thereby enabling one to better understand the…
The connection of Taylor maps and polynomial neural networks (PNN) to solve ordinary differential equations (ODEs) numerically is considered. Having the system of ODEs, it is possible to calculate weights of PNN that simulates the dynamics…
We apply the proper orthogonal decomposition (POD) to the nonlinear Schr\"odinger (NLS) equation to derive a reduced order model. The NLS equation is discretized in space by finite differences and is solved in time by structure preserving…
We obtain exact moving and stationary, spatially periodic and localized solutions of a generalized discrete nonlinear Schr\"odinger equation. More specifically, we find two different moving periodic wave solutions and a localized moving…
In this work, we introduce a novel numerical method for solving initial value problems associated with a given differential. Our approach utilizes a spline approximation of the theoretical solution alongside the integral formulation of the…
In this paper we propose a new numerical method for solving stochastic differential equations (SDEs). As an application of this method we propose an explicit numerical scheme for a super linear SDE for which the usual Euler scheme diverges.
Dynamical systems see widespread use in natural sciences like physics, biology, chemistry, as well as engineering disciplines such as circuit analysis, computational fluid dynamics, and control. For simple systems, the differential…
We consider multiple solutions to the nonlinear Schr\"odinger equation (NLS) with a partial confinement, which is physically relevant to dynamics of the Bose-Einstein condensate. Our study not only verifies the existence of positive ground…
This work investigates the long time asymptotic behavior of some inhomogeneous non-linear Schr\"odinger type equations. We give sharp a threshold of scattering versus non-scattering of mass solutions, depending on the source term. This work…
We have presented some practical consequences on the molecular-dynamics simulations arising from the numerical algorithm published recently in paper Int. J. Mod. Phys. C 16, 413 (2005). The algorithm is not a finite-difference method and…
We present a numerical method for computing optimal transition pathways and transition rates in systems of stochastic differential equations (SDEs). In particular, we compute the most probable transition path of stochastic equations by…
The nonlinear Schr\"odinger equation (NLSE) is a rich and versatile model, which in one spatial dimension has stationary solutions similar to those of the linear Schr\"odinger equation as well as more exotic solutions such as solitary waves…
Recent work has introduced a simple numerical method for solving partial differential equations (PDEs) with deep neural networks (DNNs). This paper reviews and extends the method while applying it to analyze one of the most fundamental…
A functional differential equation related to the logistic equation is studied by a combination of numerical and perturbation methods. Parameter regions are identified where the solution to the nonlinear problem is approximated well by…
This paper addresses the challenging numerical simulation of nonlinear hybrid stochastic functional differential equations with infinite delays. We first propose an explicit scheme using space and time truncation, requiring only finite…
We discuss averaging for dispersion-managed nonlinear Schr\"odinger equations in the fast dispersion management regime, with an application to the problem of constructing soliton-like solutions to dispersion-managed nonlinear Schr\"odinger…
Modelling is an essential procedure in analyzing and controlling a given logical dynamic system (LDS). It has been proved that deterministic LDS can be modeled as a linear-like system using algebraic state space representation. However, due…
In applied sciences, we often deal with deterministic simulation models that are too slow for simulation-intensive tasks such as calibration or real-time control. In this paper, an emulator for a generic dynamic model, given by a system of…