  Numerical simulations of the complex cubic-quintic Ginzburg-Landau equation
(CCQGLE), a canonical equation governing the weakly nonlinear behavior of
dissipative systems in a wide variety of disciplines, reveal five entirely
novel classes of pulse or solitary waves solutions, viz. pulsating, creeping,
snaking, erupting, and chaotical solitons. Here, we develop a theoretical
framework for analyzing the full spatio-temporal structure of one class of
dissipative solution (snaking soliton) of the CCQGLE using the variational
approximation technique and the dynamical systems theory. The qualitative
behavior of the snaking soliton is investigated using the numerical simulations
of (a) the full nonlinear complex partial differential equation and (b) a
system of three ordinary differential equations resulting from the variational
approximation.
