The three-component coupled nonlinear Schrödinger equation: Rogue waves on a multi-soliton background and dynamics

In this work, the three-component coupled nonlinear Schrödinger (tc-CNLS) equation is systemically investigated. By using the Darboux transformation, the new breather wave and rogue wave solutions of the tc-CNLS equation are constructed. These solutions exhibit breather waves and rogue waves on a multi-soliton background. Furthermore, the dynamic behaviors of these solutions are analyzed with some graphics. Our results can be of much importance in enriching and predicting rogue wave phenomena arising in nonlinear wave fields.