Abstract
For the generalized cubic Schrodinger equation, we consider a periodic boundary value problem in the case of n independent space variables. For this boundary value problem, there exists a countable set of plane running waves periodic with respect to the time variable. We analyze their stability and local bifurcations under the change of stability. We show that invariant tori of dimension 2, ..., n + 1 can bifurcate from each of them. We obtain asymptotic formulas for the solutions on invariant tori and stability conditions for bifurcating tori as well as parameter ranges in which, starting from n = 3, a subcritical (stiff) bifurcation of invariant tori is possible.
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