Optical Solitons in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">N</mml:mi></mml:math>-Coupled Higher Order Nonlinear Schrödinger Equations

Abstract

We consider the coupled higher order nonlinear Schr\"odinger (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 $2\ifmmode\times\else\texttimes\fi{}2$ Ablowitz-Kaup-Newell-Segur method to the $5\ifmmode\times\else\texttimes\fi{}5$ eigenvalue problem and construct the Lax pair. The exact soliton solutions are explicitly obtained using the Darboux-B\"acklund transformation. A similar case of study is extended to three coupled HNLS equations and hence generalized to $N$-coupled equations.