Displaying similar documents to “Darboux transformation for the nonstationary Schrödinger equation.”

Solitons and large time behavior of solutions of a multidimensional integrable equation

Anna Kazeykina (2013)

Journées Équations aux dérivées partielles

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Novikov-Veselov equation is a (2+1)-dimensional analog of the classic Korteweg-de Vries equation integrable via the inverse scattering translform for the 2-dimensional stationary Schrödinger equation. In this talk we present some recent results on existence and absence of algebraically localized solitons for the Novikov-Veselov equation as well as some results on the large time behavior of the “inverse scattering solutions” for this equation.

Resolvent and Scattering Matrix at the Maximum of the Potential

Alexandrova, Ivana, Bony, Jean-François, Ramond, Thierry (2008)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 35P25, 81U20, 35S30, 47A10, 35B38. We study the microlocal structure of the resolvent of the semiclassical Schrödinger operator with short range potential at an energy which is a unique non-degenerate global maximum of the potential. We prove that it is a semiclassical Fourier integral operator quantizing the incoming and outgoing Lagrangian submanifolds associated to the fixed hyperbolic point. We then discuss two applications of...

Dunkl-Schrödinger Equations with and without Quadratic Potentials

Mejjaoli, Hatem (2011)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: Primary 42A38. Secondary 42B10. The purpose of this paper is to study the dispersive properties of the solutions of the Dunkl-Schrödinger equation and their perturbations with potential. Furthermore, we consider a few applications of these results to the corresponding nonlinear Cauchy problems.

On solutions of the Schrödinger equation with radiation conditions at infinity : the long-range case

Yannick Gâtel, Dimitri Yafaev (1999)

Annales de l'institut Fourier

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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.

Weak Asymptotics for Schrödinger Evolution

S. A. Denisov (2010)

Mathematical Modelling of Natural Phenomena

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In this short note, we apply the technique developed in [Math. Model. Nat. Phenom., 5 (2010), No. 4, 122-149] to study the long-time evolution for Schrödinger equation with slowly decaying potential.