Soliton molecules, breather molecules and stability analysis of the three-coupled nonlinear Schrödinger equation

Abstract

Abstract We investigate the three-coupled nonlinear Schrödinger (NLS) equation, which holds a significant physical implications in optical communications and biophysics. The multi-soliton solutions are derived utilizing the Hirota bilinear method. Multi-breather solutions are presented by assuming certain relationship for the parameters of the multi-solitons. By introducing the velocity resonance mechanism to multiple soliton/breather solutions, it is found that the three-coupled NLS model possesses abundant soliton molecule, breather molecule and breather-soliton molecule structures. 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 three-coupled NLS equation is analyzed. It is highly significance for the study of soliton formation and rogue waves in the three-coupled NLS equation.