High-order compact splitting multisymplectic method for the coupled nonlinear Schrödinger equations
نویسندگان
چکیده
In this paper, we develop a new kind of multisymplectic integrator for the coupled nonlinear Schrödinger (CNLS) equations. The CNLS equations are cast into multisymplectic formulation. Then it is split into a linear multisymplectic formulation and a nonlinear Hamiltonian system. The space of the linear subproblem is approximated by a highorder compact (HOC) method which is new in multisymplectic context. The nonlinear subproblem is integrated exactly. For splitting and approximation, we utilize an HOC–SMS integrator. Its stability and conservation laws are investigated in theory. Numerical results are presented to demonstrate the accuracy, conservation laws, and to simulate various solitons as well, for the HOC–SMS integrator. They are consistent with our theoretical analysis. © 2010 Elsevier Ltd. All rights reserved.
منابع مشابه
On multisymplecticity of partitioned Runge–Kutta and splitting methods
Although Runge–Kutta and partitioned Runge–Kutta methods are known to formally satisfy discrete multisymplectic conservation laws when applied to multi-Hamiltonian PDEs, they do not always lead to well-defined numerical methods. We consider the case study of the nonlinear Schrödinger equation in detail, for which the previously known multisymplectic integrators are fully implicit and based on t...
متن کاملOn the multisymplecticity of partitioned Runge-Kutta and splitting methods
Although Runge–Kutta and partitioned Runge–Kutta methods are known to formally satisfy discrete multisymplectic conservation laws when applied to multi-Hamiltonian PDEs, they do not always lead to well-defined numerical methods. We consider the case study of the nonlinear Schrödinger equation in detail, for which the previously known multisymplectic integrators are fully implicit and based on t...
متن کاملError Analysis of High-order Splitting Methods for Nonlinear Evolutionary Schrödinger Equations and Application to the Mctdhf Equations in Electron Dynamics
In this work, the error behaviour of high-order exponential operator splitting methods for the time integration of nonlinear evolutionary Schrödinger equations is investigated. The theoretical analysis utilises the framework of abstract evolution equations on Banach spaces and the formal calculus of Lie derivatives. The general approach is substantiated on the basis of a convergence result for ...
متن کاملConvergence Analysis of High-Order Time-Splitting Pseudospectral Methods for Nonlinear Schrödinger Equations
In this work, the issue of favorable numerical methods for the space and time discretization of low-dimensional nonlinear Schrödinger equations is addressed. The objective is to provide a stability and error analysis of high-accuracy discretizations that rely on spectral and splitting methods. As a model problem, the time-dependent Gross–Pitaevskii equation arising in the description of Bose–Ei...
متن کاملHigher order exponential time differencing scheme for system of coupled nonlinear Schrödinger equations
The coupled nonlinear Schrödinger equations are highly used in modeling the various phenomena in nonlinear fiber optics, like propagation of pulses. Efficient and reliable numerical schemes are required for analysis of these models and for improvement of the fiber communication system. In this paper, we introduce a new version of the Cox and Matthews third order exponential time differencing Ru...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Computers & Mathematics with Applications
دوره 61 شماره
صفحات -
تاریخ انتشار 2011