Asymptotic stability of small solitary waves for nonlinear Schrodinger equations with electromagnetic potential in R-3

作者：Koo Eva^*

来源：Journal of Differential Equations, 2011, 250(8): 3473-3503.

DOI：10.1016/j.jde.2010.12.011

We consider the nonlinear magnetic Schrodinger equation for u : R-3 x R -> C,
iu(t) = (i del + A)(2)u + Vu + g(u), u(x, 0) = u(0)(x),
where A : R-3 -> R-3 is the magnetic potential, V : R-3 -> R is the electric potential, and g = +/-vertical bar u vertical bar(2)u is the nonlinear term. We show that under suitable assumptions on the electric and magnetic potentials, if the initial data is small enough in H-1. then the solution of the above equation decomposes uniquely into a standing wave part, which converges as t -> infinity and a dispersive part, which scatters.

• 出版日期2011-4-15