P.G. Kevrekidis, D. Pelinovsky, and A. Stefanov
Nonlinearity management in higher dimensions
Journal of Physics A: Mathematical General 39, 479-488 (2006)
In the present short communication, we revisit nonlinearity management of the
time-periodic nonlinear Schrodinger equation and the related
averaging procedure. We prove that the averaged nonlinear
Schrodinger equation does not support the blow-up of solutions
in higher dimensions, independently of the strength in the
nonlinearity coefficient variance. This conclusion agrees with
earlier works in the case of strong nonlinearity management but
contradicts those in the case of weak nonlinearity management.
The apparent discrepancy is explained by the divergence of the averaging
procedure in the limit of weak nonlinearity management.
TIME-PERIODIC NONLINEAR SCHRODINGER EQUATION, NONLINEARITY MANAGEMENT, AVERAGED EQUATIONS,
BLOWUP OF SOLUTIONS, LOCAL AND GLOBAL WELL-POSEDNESS