#### Title

On the long-time limit of semiclassical (zero dispersion limit) solutions of the focusing nonlinear Schrodinger equation: Pure radiation case

#### Abbreviated Journal Title

Commun. Pure Appl. Math.

#### Keywords

ASYMPTOTICS; Mathematics, Applied; Mathematics

#### Abstract

In a previous paper [13] we calculated the leading-order term q(0)(x, t, epsilon) of the solution of q (x, t, epsilon), the focusing nonlinear (cubic) Schrodinger (NLS) equation in the semiclassical limit (epsilon -> 0) 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 >= 0. The aim of the present paper is to calculate the long-term behavior of the semiclassical solution q(x, t, epsilon) in. the pure radiation case. As before, our main tool is the Riemann-Hilbert problem (RHP) formulation of the inverse scattering problem and the corresponding system of "moment and integral conditions," known also as a system of "modulation equations." (c) 2006 Wiley Periodicals, Inc.

#### Journal Title

Communications on Pure and Applied Mathematics

#### Volume

59

#### Issue/Number

10

#### Publication Date

1-1-2006

#### Document Type

Article

#### DOI Link

#### Language

English

#### First Page

1379

#### Last Page

1432

#### WOS Identifier

#### ISSN

0010-3640

#### Recommended Citation

"On the long-time limit of semiclassical (zero dispersion limit) solutions of the focusing nonlinear Schrodinger equation: Pure radiation case" (2006). *Faculty Bibliography 2000s*. 6654.

http://stars.library.ucf.edu/facultybib2000/6654

## Comments

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