Stability of exact solutions of the cubic-quintic nonlinear Schrödinger equation with periodic potential

Abstract

The nonlinear Schrödinger equation with attractive quintic nonlinearity in periodic potential in 1D, modeling a dilute-gas Bose-Einstein condensate in a lattice potential, is considered and one family of exact stationary solutions is discussed. Some of these solutions have an analog neither in the linear Schrödinger equation nor in the integrable nonlinear Schrödinger equation. Their stability is examined analytically and numerically.