  Recently, we have shown that the Manakov equation can admit a more general
class of nondegenerate vector solitons, which can undergo collision without any
intensity redistribution in general among the modes, associated with distinct
wave numbers, besides the already known energy exchanging solitons
corresponding to identical wave numbers. In the present comprehensive paper, we
discuss in detail the various special features of the reported nondegenerate
vector solitons. To bring out these details, we derive the exact forms of such
vector one-, two- and three-soliton solutions through Hirota bilinear method
and they are rewritten in more compact forms using Gram determinants. The
presence of distinct wave numbers allows the nondegenerate fundamental soliton
to admit various profiles such as double-hump, flat-top and single-hump
structures. We explain the formation of double-hump structure in the
fundamental soliton when the relative velocity of the two modes tends to zero.
More critical analysis shows that the nondegenerate fundamental solitons can
undergo shape preserving as well as shape altering collisions under appropriate
conditions. The shape changing collision occurs between the modes of
nondegenerate solitons when the parameters are fixed suitably. Then we observe
the coexistence of degenerate and nondegenerate solitons when the wave numbers
are restricted appropriately in the obtained two-soliton solution. In such a
situation we find the degenerate soliton induces shape changing behavior of
nondegenerate soliton during the collision process. By performing suitable
asymptotic analysis we analyze the consequences that occur in each of the
collision scenario. Finally we point out that the previously known class of
energy exchanging vector bright solitons, with identical wave numbers, turns
out to be a special case of the newly derived nondegenerate solitons.
