 
Summary: A Numerical Study of the Semiclassical Limit of the
Focusing Nonlinear Schrodinger Equation
Hector D. Ceniceros
Department of Mathematics, University of California, Santa Barbara, CA 93106
hdc@math.ucsb.edu
FeiRan Tian
Department of Mathematics, The Ohio State University, Columbus, OH 43210
tian@math.ohiostate.edu
Abstract
We study the solution of the focusing nonlinear Schrodinger equation in the semi
classical limit. Numerical solutions are presented for four dierent 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.
x 1 Introduction
Many dynamics in nature undergo dispersive processes, while the dissipative or
diusive 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
