The existence of countably many stable cycles for a generalized cubic Schrodinger equation in a planar domain

摘要

We consider the boundary- value problem u_t + iΔu = ε(u - d|u|~2u), u|(partial deriv)_Ω = 0, in the domain Ω = {(x,y):0 ≤ x ≤ 1, 0 ≤ y ≤ 1}, where u is a complex-valued function, A is the Laplace operators, 0 < ε 1 and d = 1 + i_(c_0), c_0 ∈R. We establish that it has countably many stable solutions that are periodic in t. We study the question of whether this phenomenon is preserved under a change of domain or boundary conditions.