Optical Solitons inN-Coupled Higher Order Nonlinear Schrödinger Equations

We consider the coupled higher order nonlinear Schrödinger (CHNLS) equations which govern the propagation of the fields in a birefringent fiber with all higher order effects like the third order dispersion, Kerr dispersion, and stimulated Raman scattering. We generalize the $2\times 2$ Ablowitz-Kaup-Newell-Segur method to the $5\times 5$ eigenvalue problem and construct the Lax pair. The exact soliton solutions are explicitly obtained using the Darboux-Bäcklund transformation. A similar case of study is extended to three coupled HNLS equations and hence generalized to $N$-coupled equations.