  By means of new general variational method we report a direct solution for
the quintic self-focusing nonlinearity and cubic-quintic 1D Gross Pitaeskii
equation (GPE) in a harmonic confined potential. We explore the influence of
the 3D transversal motion generating a quintic nonlinear term on the ideal 1D
pure cigar-like shape model for the attractive and repulsive atom-atom
interaction in Bose Einstein condensates (BEC). Also, we offer a closed
analytical expression for the evaluation of the error produced when solely the
cubic nonlinear GPE is considered for the description of 1D BEC.
