Inverse scattering approach to coupled higher order nonlinear Schr\"odinger equation and N-soliton solutions

A generalized inverse scattering method has been applied to the linear problem associated with the coupled higher order nonlinear schr"odinger equation to obtain it’s $N$-soliton solution. An infinite number of conserved quantities have been obtained by solving a set of coupled Riccati equations. It has been shown that the coupled system admits two different class of solutions, characterised by the number of local maxima of amplitude of the soliton.