Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential

AbstractWe prove that the Schrödinger equation with potential V and cubic nonlinearity ih̵ψt = −(h̵22m)ψxx + Vψ − γ¦ψ¦2ψ has standing wave solutions concentrated near each nondegenerate critical point of V if γ > 0, V is bounded, and h̵ is sufficiently small