Type: Article

Upper and lower time decay bounds for solutions of dissipative nonlinear Schrödinger equations

Hayashi, N, Lic C, Naumkin P. I;

Abstract:

We study the upper and lower time decay bounds for solutions of dissipative nonlinear Schrodinger equations { i partial derivative(i)u + 1/2 Delta u = lambda vertical bar u vertical bar(p-1) u, (t, x) is an element of R+ x R-n, u(0, x) =u(0) (x), x is an element of R-n in space dimensions n = 1, 2 or 3, where lambda = lambda(1) + i lambda(2), lambda(j) is an element of R, j = 1, 2, lambda(2) < 0 and the subcritical order of nonlinearity p = 1 + 2/n - u, where mu > 0 is small enough.