Semiclassical Focusing Nonlinear Schrodinger Equation I: Inverse scattering map and its evolution for radiative initial data
نویسندگان
چکیده
منابع مشابه
Inverse scattering transform for the integrable discrete nonlinear Schrodinger equation
The inverse scattering transform for an integrable discretization of the defocusing nonlinear Schrodinger equation with nonvanishing boundary values at infinity is constructed. This problem had been previously studied, and many key results had been established. Here, a suitable transformation of the scattering problem is introduced in order to address the open issue of analyticity of eigenfunct...
متن کاملInverse scattering problem for the Impulsive Schrodinger equation with a polynomial spectral dependence in the potential
In the present work, under some di¤erentiability conditions on the potential functions , we rst reduce the inverse scattering problem (ISP) for the polynomial pencil of the Scroedinger equation to the corresponding ISP for the generalized matrix Scrödinger equation . Then ISP will be solved in analogy of the Marchenko method. We aim to establish an e¤ective algorithm for uniquely reconstructin...
متن کاملOn the semi-classical limit for the focusing nonlinear Schrodinger equation: sensitivity to analytic properties of the initial data
We present the results of a large number of careful numerical experiments carried out to investigate the way that the solution of the integrable focusing nonlinear Schrodinger equation with xed initial data, when taken to be close to the semiclassical limit, depends on analyticity properties of the data. In particular, we study a family of initial data that have complex singularities at an a...
متن کاملSemiclassical limit of the scattering transform for the focusing Nonlinear Schrödinger Equation
X iv :0 90 3. 26 48 v1 [ m at hph ] 1 5 M ar 2 00 9 Abstract. The semiclassical limit of the focusing Nonlinear (cubic) Schrödinger Equation (NLS) corresponds to the singularly perturbed Zakharov Shabat (ZS) system that defines the direct and inverse scattering transforms (IST). In this paper, we derive explicit expressions for the leading order terms of these transforms, which are called semic...
متن کاملScattering and inverse scattering for the 1-D SchrOdinger equation witti energy-dependent potentials
The one-dimensional Schriidinger equation with a potential k2 V( X) proportional to energy is studied. This equation is equivalent to the wave equation with variable speed. When V(X) < 1, is bounded below, and satisfies two integrability conditions, the scattering matrix is obtained and its asymptotics for small and large energies are established. The inverse scattering problem of recovering V(...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2010
ISSN: 1073-7928,1687-0247
DOI: 10.1093/imrn/rnm094