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Physics Letters A 306 (2002) 2534 www.elsevier.com/locate/pla
 

Summary: Physics Letters A 306 (2002) 25­34
www.elsevier.com/locate/pla
A numerical study of the semi-classical limit of the focusing
nonlinear Schrödinger equation
H.D. Ceniceros a
, Fei-Ran Tian b,
a Department of Mathematics, University of California, Santa Barbara, CA 93106, USA
b Department of Mathematics, The Ohio State University, Columbus, OH 43210, USA
Received 10 July 2000; received in revised form 8 December 2000; accepted 11 December 2000
Communicated by A.P. Fordy
Abstract
We study the solution of the focusing nonlinear Schrödinger equation in the semiclassical limit. Numerical solutions are
presented for four different kinds of initial data, of which three are analytic and one is nonanalytic. We verify numerically the
weak convergence of the oscillatory solution by examining the strong convergence of the spatial average of the solution.
2002 Elsevier Science B.V. All rights reserved.
1. Introduction
Many dynamics in nature undergo dispersive pro-
cesses, while the dissipative or diffusive mechanisms
are negligible [23,30]. Examples include the vortex
sheet problem of incompressible fluids [16], plasmas

  

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

 

Collections: Mathematics