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A Numerical Study of the Semi-classical Limit of the Focusing Nonlinear Schrodinger Equation
 

Summary: A Numerical Study of the Semi-classical Limit of the
Focusing Nonlinear Schrodinger Equation
Hector D. Ceniceros
Department of Mathematics, University of California, Santa Barbara, CA 93106
hdc@math.ucsb.edu
Fei-Ran Tian
Department of Mathematics, The Ohio State University, Columbus, OH 43210
tian@math.ohio-state.edu
Abstract
We study the solution of the focusing nonlinear Schrodinger equation in the semi-
classical limit. Numerical solutions are presented for four di erent kinds of initial
data, of which three are analytic and one is non-analytic. We verify numerically the
weak convergence of the oscillatory solution by examining the strong convergence of
the spatial average of the solution.

x 1 Introduction
Many dynamics in nature undergo dispersive processes, while the dissipative or
di usive mechanisms are negligible [23, 30]. Examples include the vortex sheet prob-
lem of incompressible uids [16], plasmas [13, 27], and certain aspects of nonlinear
optics [11, 20]. When the dispersive parameter is small, there appear regions in

  

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

 

Collections: Mathematics