The algebraic method is developed to obtain new exact solutions, including stationary wave solutions and traveling wave solutions, for the cubic-quintic nonlinear Schrödinger (NLS) equation. Specifically, we present two general solution formulae, which degenerate to the corresponding solution of the cubic NLS equation, when the quintic nonlinear term is absent. It is expected that they are useful in correlative physics fields.
"New exact solutions for the cubic-quintic nonlinear Schrödinger equation." Commun. Math. Sci. 5 (2) 243 - 252, June 2007.