On a Class of non Linear Schrödinger Equations with non Local Interaction.
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Jean Ginibre, Giorgio Velo (1980)
Mathematische Zeitschrift
Günter Stolz, Thomas Poerschke (1993)
Mathematische Zeitschrift
Roman G. Novikov (2006)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
We develop the -approach to inverse scattering at zero energy in dimensions of [Beals, Coifman 1985], [Henkin, Novikov 1987] and [Novikov 2002]. As a result we give, in particular, uniqueness theorem, precise reconstruction procedure, stability estimate and approximate reconstruction for the problem of finding a sufficiently small potential in the Schrödinger equation from a fixed non-overdetermined (“backscattering” type) restriction of the Faddeev generalized scattering amplitude in the...
Michael Demuth (1982)
Banach Center Publications
Yannick Gâtel, Dimitri Yafaev (1999)
Annales de l'institut Fourier
We consider the homogeneous Schrödinger equation with a long-range potential and show that its solutions satisfying some a priori bound at infinity can asymptotically be expressed as a sum of incoming and outgoing distorted spherical waves. Coefficients of these waves are related by the scattering matrix. This generalizes a similar result obtained earlier in the short-range case.
Gurappa, N., Jha, Pankaj K., Panigrahi, Prasanta K. (2007)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
Kalyan B. Sinha, M. Krishna, Pl. Muthuramalingam (1984)
Annales de l'I.H.P. Physique théorique
G. Auberson, G. Mennessier (1979)
Annales de l'I.H.P. Physique théorique
Riccardo Adami (2005)
Bollettino dell'Unione Matematica Italiana
This article reflects in its content the talk the author gave at the XVII Congresso dellUnione Matematica Italiana, held in Milano, 8-13 September 2003. We review about some recent results on the problem of deriving the Gross-Pitaevskii equation in dimension one from the dynamics of a quantum system with a large number of identical bosons. We explain the motivations for some peculiar choices (shape of the interaction potential, scaling, initial datum). Open problems are pointed out and difficulties...
D. R. Yafaev (1988/1989)
Séminaire Équations aux dérivées partielles (Polytechnique)
A. V. Sobolev, D. R. Yafaev (1986)
Annales de l'I.H.P. Physique théorique
D. Yafaev (1992/1993)
Publications mathématiques et informatique de Rennes
Robert Alicki (1981)
Annales de l'I.H.P. Physique théorique
Kellendonk, Johannes, Richard, Serge (2008)
Mathematical Physics Electronic Journal [electronic only]
N. Lerner, D. Yafaev (1995/1996)
Séminaire Équations aux dérivées partielles (Polytechnique)
Xue Ping Wang (1985)
Publications mathématiques et informatique de Rennes
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