Energy-conserving methods for the nonlinear Schrödinger equation
نویسندگان
چکیده
منابع مشابه
Energy-conserving methods for the nonlinear Schrödinger equation
In this paper, we further develop recent results in the numerical solution of Hamiltonian partial differential equations (PDEs) [14], by means of energyconserving methods in the class of Line Integral Methods, in particular, the Runge-Kutta methods named Hamiltonian Boundary Value Methods (HBVMs). We shall use HBVMs for solving the nonlinear Schrödinger equation (NLSE), of interest in many appl...
متن کاملStroboscopic Averaging for the Nonlinear Schrödinger Equation
In this paper, we are concerned with an averaging procedure, – namely Stroboscopic averaging [SVM07, CMSS10] –, for highly-oscillatory evolution equations posed in a (possibly infinite dimensional) Banach space, typically partial differential equations (PDEs) in a high-frequency regime where only one frequency is present. We construct a highorder averaged system whose solution remains exponenti...
متن کاملOpen boundaries for the nonlinear Schrödinger equation
We present a new algorithm, the Time Dependent Phase Space Filter (TDPSF) which is used to solve time dependent Nonlinear Schrodinger Equations (NLS). The algorithm consists of solving the NLS on a box with periodic boundary conditions (by any algorithm). Periodically in time we decompose the solution into a family of coherent states. Coherent states which are outgoing are deleted, while those ...
متن کاملBarrier transmission for the Nonlinear Schrödinger Equation : Engineering nonlinear transport
In this communication we report on a peculiar property of barrier transmission that systems governed by the nonlinear Schrödinger equation share with the linear one: For unit transmission the potential can be divided at an arbitrary point into two sub-potentials, a left and a right one, which have exactly the same transmission. This is a rare case of an exact property of a nonlinear wave functi...
متن کاملBreathers for the Discrete Nonlinear Schrödinger Equation with Nonlinear Hopping
We discuss the existence of breathers and lower bounds on their power, in nonlinear Schrödinger lattices with nonlinear hopping. Our methods extend from a simple variational approach to fixed-point arguments, deriving lower bounds for the power which can serve as a threshold for the existence of breather solutions. Qualitatively, the theoretical results justify non-existence of breathers below ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Applied Mathematics and Computation
سال: 2018
ISSN: 0096-3003
DOI: 10.1016/j.amc.2017.04.018