Difference schemes for solving the generalized nonlinear Schrödinger equation
type: Item
instance of: scholarly article
title: Difference schemes for solving the generalized nonlinear Schrödinger equation
zbMATH Open document ID: 0923.65059
author: Erhui Jia
author: Qianshun Chang
author: Weiwei Sun
published in: Journal of Computational Physics
publication date: 1999-10-17T00:00:00Z
review text: The authors study different finite difference schemes for solving the generalized nonlinear Schrödinger (GNLS) equation \[ iu_t - u_x u + q(| u| ^2) u = f(x,t)u. \] A new linearized Crank-Nicolson-type scheme is presented by applying an extrapolation technique to the real coefficients of the nonlinear terms in the GNLS equations. Three particular model situations with \[ q(s) = s^2, \qquad q(s) = \ln(1+s), \qquad q(s) = -4s/(1+s) \] are studied. The authors present results of numerical experiments, where the proposed scheme is compared with other Crank-Nicolson-type schemes, Hopscotch-type schemes, split step Fourier schemes, and with spectral schemes. The numerical experiments presented at the end of the paper demonstrate the efficiency and robustness of the proposed linearized Crank-Nicolson scheme for solving GNLS equations.
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 35Q55
zbMATH DE Number: 1271998
zbMATH Keywords: difference schemes
zbMATH Keywords: comparison of methods
zbMATH Keywords: linearized Crank-Nicolson scheme
zbMATH Keywords: generalized nonlinear Schrödinger equation
zbMATH Keywords: extrapolation
zbMATH Keywords: numerical experiments
MaRDI profile type: Publication
full work available at URL: jcph.1998.6120
OpenAlex ID: W2015186260
cites work: Gaussons: Solitons of the Logarithmic Schrödinger Equation
cites work: Solitons in Laser Physics
cites work: Q3668789
cites work: Multigrid and adaptive algorithm for solving the nonlinear Schrödinger equation
cites work: Q3735028
cites work: Pseudo-spectral solution of nonlinear Schrödinger equations
cites work: Q3205693
cites work: Numerical simulation of singular solutions to the two-dimensional cubic schrödinger equation
cites work: Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical, nonlinear Schrödinger equation
cites work: A numerical and theoretical study of certain nonlinear wave phenomena
DOI: 10.1006/JCPH.1998.6120
description: scientific article; zbMATH DE number 1271998