Superregular solutions for a coupled nonlinear Schrödinger system in a two-mode nonlinear fiber

Abstract

Abstract For the increase of the transmission capacity in optical communication systems, the so-called few-mode fibers are used for people to design the mode division multiplexing transmission. In this paper, we analytically obtain and graphically display the superregular solutions for a coupled nonlinear Schrödinger (NLS) system which describes the wave evolution in a two-mode nonlinear fiber, where the superregular solutions are the analogue of superregular breathers for certain scalar NLS-type equations. On the nonzero-zero (or proportional nonzero-nonzero) background, regular solutions describe the regular nonlinear waves which are located in a finite t domain but do not perturb the background with t being big enough, and superregular solutions are a subset of regular solutions which describe the nonlinear superposition of breathers and dark-bright (or breather-like) solitons developing from the perturbations on the dark-bright (or breather-like) solitons at a certain z, where z and t denote the evolution dimension and temporal distribution dimension, respectively. On the nonzero-zero background, superregular solutions are constructed in three cases: trivial case, a pair of breathers case and single breather case, and then other superregular solutions could be constructed according to the analyses for such three cases. Superregular solutions on the proportional nonzero-nonzero background are derived via the superregular solutions on the nonzero-zero background and an orthogonal transformation.