  We show the complete integrability and the existence of optical solitons of
higher order nonlinear Schrodinger equation by inverse scattering method for a
wide range of values of coefficients. This is achieved first by invoking a
novel connection between the integrability of a nonlinear evolution equation
and the dimensions of a family of matrix Lax pairs. It is shown that Lax pairs
of different dimensions lead to the same evolution equation only with the
coefficients of the terms in different integer ratios. Optical solitons, thus
obtained by inverse scattering method, have been found by solving an n
dimensional eigenvalue problem.
