Related papers: High order exponential integrators for nonlinear S…
In this paper we present a novel class of asymptotic consistent exponential-type integrators for Klein-Gordon-Schr\"odinger systems that capture all regimes from the slowly varying classical regime up to the highly oscillatory…
The numerical integration of the Schr\"odinger equation by discretization of time is explored for the curved manifolds arising from finite representations based on evolving basis states. In particular, the unitarity of the evolution is…
We study an example of exact parametric resonance in a extended system ruled by nonlinear partial differential equations of nonlinear Schr\"odinger type. It is also conjectured how related models not exactly solvable should behave in the…
In this paper we deal with a nonlinear Schr\"{o}dinger equation with chaotic, random, and nonperiodic cubic nonlinearity. Our goal is to study the soliton evolution, with the strength of the nonlinearity perturbed in the space and time…
Correlation functions of exactly solvable models can be described by differential equation [Barough, McCoy, Wu]. In this paper we show that for non free fermionic case differential equations should be replaced by integro-differential…
A typical procedure to integrate numerically the time dependent Schr\"o\-din\-ger equation involves two stages. In the first one carries out a space discretization of the continuous problem. This results in the linear system of differential…
A Bose-Einstein condensation theory for any integer spin using noncommutative quantum mechanics methods is considered. The effective potential is derived as a multipolar expansion in the non-commutativity parameter ($\theta$) and, at second…
The present work provides a comprehensive study of symmetric-conjugate operator splitting methods in the context of linear parabolic problems and demonstrates their additional benefits compared to symmetric splitting methods. Relevant…
Utilization of a quantum system whose time-development is described by the nonlinear Schrodinger equation in the transformation of qubits would make it possible to construct quantum algorithms which would be useful in a large class of…
This paper introduces filtered finite difference methods for numerically solving a dispersive evolution equation with solutions that are highly oscillatory in both space and time. We consider a semiclassically scaled nonlinear Schr\"odinger…
We show that the method of splitting the operator ${\rm e}^{\epsilon(T+V)}$ to fourth order with purely positive coefficients produces excellent algorithms for solving the time-dependent Schr\"odinger equation. These algorithms require…
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…
We introduce a new methodology based on the multirevolution idea for constructing integrators for stochastic differential equations in the situation where the fast oscillations themselves are driven by a Stratonovich noise. Applications…
This paper introduces weighted finite difference methods for numerically solving dispersive evolution equations with solutions that are highly oscillatory in both space and time. We consider a semiclassically scaled cubic nonlinear…
In this paper, an exact unitary transformation is examined that allows for the construction of solutions of coupled nonlinear Schr{\"o}dinger equations with additional linear field coupling, from solutions of the problem where this linear…
This paper describes an updated exponential Fourier based split-step method that can be applied to a greater class of partial differential equations than previous methods would allow. These equations arise in physics and engineering, a…
We use a change of variables that turns the critical nonlinear Schroedinger equation into the critical nonlinear Schroedinger equation with isotropic harmonic potential, in any space dimension. This change of variables is isometric on…
In this paper a technique is suggested to integrate linear initial boundary value problems with exponential quadrature rules in such a way that the order in time is as high as possible. A thorough error analysis is given for both the…
This paper addresses the problem of efficiently computing higher-order variational integrators in simulation and trajectory optimization of mechanical systems as those often found in robotic applications. We develop $O(n)$ algorithms to…
We study a deformation of the nonlinear Schr\"odinger equation recently derived in the context of deformation of hierarchies of integrable systems. This systematic method also led to known integrable equations such as the Camassa-Holm…