Semiclassical resolvent estimates
We extend the results in [5] to non-compactly supported perturbations for a class of symmetric first order systems.
Small data scattering for nonlinear Schrödinger equations (NLS), nonlinear wave equations (NLW), nonlinear Klein-Gordon equations (NLKG) with power type nonlinearities is studied in the scheme of Sobolev spaces on the whole space with order . The assumptions on the nonlinearities are described in terms of power behavior at zero and at infinity such as for NLS and NLKG, and for NLW.
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.