On semiclassical (zero dispersion limit) solutions of the focusing nonlinear Schrodinger equation
Abbreviated Journal Title
Commun. Pure Appl. Math.
KORTEWEG-DEVRIES EQUATION; VARYING EXPONENTIAL WEIGHTS; SHABAT; EIGENVALUE PROBLEM; ASYMPTOTICS; POLYNOMIALS; RESPECT; GENERATION; POTENTIALS; Mathematics, Applied; Mathematics
We calculate the leading-order term of the solution of the focusing nonlinear (cubic) Schrodinger equation (NLS) in the semiclassical limit for a certain one-parameter family of initial conditions. This family contains both solitons and pure radiation. In the pure radiation case, our result is valid for all times t greater than or equal to 0. We utilize the Riemann-Hilbert problem formulation of the inverse scattering problem to obtain the leading-order term of the solution. Error estimates are provided. (C) 2004 Wiley Periodicals, Inc.
Communications on Pure and Applied Mathematics
"On semiclassical (zero dispersion limit) solutions of the focusing nonlinear Schrodinger equation" (2004). Faculty Bibliography 2000s. 4837.