With a variational method, we study the cubic-quintic nonlinear Schrödinger equation for pulse propagation in optical fibers. Anomalous dispersion that gives rise to fundamental bright solitary waves is considered. It is shown that within the specified limits, the present variational model demonstrates (for 1 picosecond pulse) good agreements with its analytical equivalent. It is proved that for negative coefficient of the fifth-order nonlinearity existence of the two-state solitary wave solution is a peculiarity of the variational formulation.

Techniques are presented for expanding a periodic function of cubic translational symmetry and arbitrary rotational symmetry in a finite set of symmetry-adapted plane waves. Results for all cubic lattices are tabulated in a form convenient for use in computation. The role of ’’special points’’ in the sense of Chadi and Cohen is discussed in the extended context of symmetry-adapted plane waves.

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