Volume 17, Number 1, Spring 2009
EXACT DARK SOLITON, PERIODIC
SOLUTIONS AND CHAOTIC DYNAMICS IN A
PERTURBED GENERALIZED NONLINEAR
Abstract. For the cubic-quintic generalized nonlinear
S chrödinger equation (GNLS), the exact dark soliton solution
and periodic solutions are given. The persistence of dark
soliton and chaotic dynamics of the traveling wave solutions for the
perturbed cubic-quintic GNLS-equation are rigorously proved.
To guarantee the existence of the above solutions, all parameter
conditions are determined.