Displaying similar documents to “Properties of the scattering map.”

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.

Scattering problems in a domain with small holes.

V. Chiadò Piat, M. Codegone (2003)

RACSAM

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In this paper, we consider a family of scattering problems in perforated unbounded domains Ω. We assume that the perforation is contained in a bounded region and that the holes have a ?critical? size. We study the asymptotic behaviour of the outgoing solutions of the steady-state scattering problem and we prove that an extra term appears in the limit equation. Finally, we obtain convergence results for scattering frequencies and solutions.