On the scattering problem for the nonlinear Schrödinger equation with a potential in 2D
Sign Up to like & getrecommendations! Published in 2019 at "Physica D: Nonlinear Phenomena"
DOI: 10.1016/j.physd.2019.03.010
Abstract: Abstract We consider the scattering problem for the nonlinear Schrodinger equation with a potential in two space dimensions. Appropriate resolvent estimates are proved and applied to estimate the operator A ( s ) appearing in… read more here.
Keywords: scattering problem; problem nonlinear; nonlinear schr; equation potential ... See more keywords
Calculation of the propagator of Schrödinger’s equation on (0, ∞) with the potential kx−2 + ω2x2 by Laplace’s method
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Mathematical Physics"
DOI: 10.1063/1.5030787
Abstract: Using Laplace’s method, Green’s function of the operator ∂t−12∂x2+k2x−2+12ω2x2,k≥−14, ω≥0 is calculated in the half-space x > 0. Therefrom, we deduce the propagator of Schrodinger’s equation with the potential V(x) = kx−2 + ω2x2 for k≥34. read more here.
Keywords: laplace method; propagator; potential 2x2; equation potential ... See more keywords