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COMMUNICATIONS ON Website: http://AIMsciences.org PURE AND APPLIED ANALYSIS
 

Summary: COMMUNICATIONS ON Website: http://AIMsciences.org
PURE AND APPLIED ANALYSIS
Volume 1, Number 4, October 2002 pp. 1­14
A SEMI-IMPLICIT MOVING MESH METHOD FOR THE
FOCUSING NONLINEAR SCHRšODINGER EQUATION
Hector D. Ceniceros
Department of Mathematics
University of California
Santa Barbara California, 93106
(Communicated by ???)
Abstract. An efficient adaptive moving mesh method for investigation of the
semi-classical limit of the focusing nonlinear Schršodinger equation is presented.
The method employs a dynamic mesh to resolve the sea of solitons observed
for small dispersion parameters. A second order semi-implicit discretization is
used in conjunction with a dynamic mesh generator to achieve a cost-efficient,
accurate, and stable adaptive scheme. This method is used to investigate with
highly resolved numerics the solution's behavior for small dispersion parame-
ters. Convincing evidence is presented of striking regular space-time patterns
for both analytic and non-analytic initial data.
1. Introduction. Consider the initial value problem for focusing nonlinear Schršodinger

  

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

 

Collections: Mathematics