Localized Wave and Dynamics Analysis in an Extended-coupling Kaup-Newell Equation

In this paper, an extended-coupling Kaup-Newell (KN) equation is derived by the compatibility condition, which can be applied in many branches of physics and mathematics, especially in the fields of optics and water waves. Subsequently, the above equation’s Lax integrability are verified. Based on Lax integrability, the N-fold Darboux transformation of the extended-coupling KN equation is constructed. After that, through Darboux transformation, we obtain localized wave solutions of the extended-coupling KN equation, including soliton and breather solutions. Finally, these exact solutions are analyzed by figures.