Plenty of novel soliton molecules and modulation instability in the coherently coupled nonlinear Schrödinger equation

Abstract

We investigate the coherently coupled nonlinear Schrödinger (NLS) equation, which can describe the propagation of two orthogonally polarized electromagnetic waves in a nonlinear fiber. The multi-soliton solutions are derived by using the Hirota bilinear method. Multi-breather solutions are presented by assuming the relationship between the parameters of the multi-solitons. Based on multi-soliton solutions and multi-breather solutions, some new interaction structures consisting of soliton molecules, breather molecules and soliton-breather molecules are found by applying the velocity resonance condition. The interactions among different types of soliton molecules, which can be observed in marine and oceanic waters, are investigated through numerical simulation. Ultimately, baseband modulation instability of the coherently coupled NLS equation is analyzed. It is of great significance for the study of soliton formation and rogue waves in the coherently coupled NLS equation.