Stability of exact solutions of the cubic-quintic nonlinear Schrödinger equation with periodic potential - Kengne, E.; Vaillancourt, R. (Нелінійні коливання, 2010)
The nonlinear Schrodinger equation with attractive quintic nonlinearity in periodic potential in 1D, modelling 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 neither an analog in the linear Schrodinger equation nor in the integrable nonlinear Schrodinger equation. Their stability is examined analytically and numerically.