Maximum norm error estimates of fourth-order compact difference scheme for the nonlinear Schrödinger equation involving a quintic term.
Hanqing Hu,Hanzhang Hu +1 more
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TLDR
The unconditional stability and convergence in maximum norm with order O(τ2+h4)$O({\tau }^{2}+h^{4})$ are proved by using the energy method.Abstract:
A compact finite difference (CFD) scheme is presented for the nonlinear Schrodinger equation involving a quintic term. The two discrete conservative laws are obtained. The unconditional stability and convergence in maximum norm with order $O({\tau }^{2}+h^{4})$
are proved by using the energy method. A numerical experiment is presented to support our theoretical results.read more
Citations
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Numerical Methods For Partial Differential Equations
TL;DR: Numerical methods for partial differential equations is available in the digital library an online access to it is set as public so you can download it instantly and is universally compatible with any devices to read.
Journal ArticleDOI
Conservative Finite-Difference Scheme for 1D Ginzburg–Landau Equation
Vyacheslav A. Trofimov,M.M. Loginova,M. V. Fedotov,Daniil Tikhvinskii,Yongqiang Yang,Boyuan Zheng +5 more
TL;DR: In this paper , a finite-difference scheme for the problem of laser pulse propagation in an optical fiber containing an optical amplifier or attenuator is presented. But the authors focus on deriving integrals of motion (conservation laws; invariants).
Journal ArticleDOI
Conservative local discontinuous Galerkin methods for the cubic-quintic nonlinear Schrödinger equation
TL;DR: The local discontinuous Galerkin methods to solve the cubic-quintic nonlinear Schrodinger equation are proposed and by choosing the appropriate numerical fluxes, the mass- and energy-conserving properties are proved for both the semi-discrete and fully discrete methods.
Journal ArticleDOI
On the convergence of finite difference scheme for a Schrödinger type equation
TL;DR: In this paper , an initial boundary value problem for the linear Schrodinger equation including the momentum operator is introduced, which is discretized by the finite difference method and a difference scheme is presented.
References
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Solitons and Nonlinear Wave Equations
TL;DR: A discussion of the theory and applications of classical solitons is presented in this paper with a brief treatment of quantum mechanical effects which occur in particle physics and quantum field theory, including solitary waves and soliton, scattering transforms, the Schroedinger equation and the Korteweg-de Vries equation.
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TL;DR: In this article, the authors presented the first experiment of all-optical solitons in a real optical fiber and showed that they can be used for information transfer in optical fibers.
Numerical Methods For Partial Differential Equations
TL;DR: Numerical methods for partial differential equations is available in the digital library an online access to it is set as public so you can download it instantly and is universally compatible with any devices to read.
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