We now generalize the notion of nonlinear waves from their
traditional stationary character (one mode of the waveguide they induce)
to the novel dynamic nonlinear wave which is composed of two
orthogonal modes of the linear waveguide it induces. It is
clear from (2), that the polarization state of this wave
changes as the wave propagates, due to modal beating. Note that
vector solitons, discussed above, result due to fortuitous
degeneracies, 
. This view of vector
solitons is physically insightful.
Taken together, (2) and (3) lead to the defining eigenvalue equation
allowing for birefringent
material (induced, and/or intrinsic) as discussed relative to
(5). However, unlike vector solitons, dynamic solitons do not
necessitate a birefringent medium unless mode `a' and `b'
are degenerate [23]. Indeed, the simplest
conceptual examples are the so-called dynamic spatial solitons
of an isotropic homogeneous medium [21] where
. Dynamic spatial solitons
embrace a large class of waves, depending on the choice of
modes in (2) and on the material properties.
Finally, by comparing (5) and (6) we observe that vector solitons in the presence of (intensity independent) linear birefringence, obey the same equations as dynamic
solitons. Although dynamic and vector solitons are physically quite different, in general, they obey the same equations.