  The well-known (1+1D) nonlinear Schr\"odinger equation (NSE) governs the
propagation of narrow-band pulses in optical fibers and others one-dimensional
structures. For exploration the evolution of broad-band optical pulses
(femtosecond and attosecond) it is necessary to use the more general nonlinear
amplitude equation (GNAE) which differs from NSE with two additional
non-paraxial terms. That is way, it is important to make clear the difference
between the solutions of these two equations. We found a new analytical soliton
solution of GNAE and compare it with the well-known NSE one. It is shown that
for the fundamental soliton the main difference between the two solutions is in
their phases. It appears that, this changes significantly the evolution of
optical pulses in multisoliton regime of propagation and admits a behavior
different from that of the higher-order NSE solitons.
