A Study on Hybrid Solutions and Their Interactions in the Extended Nonlinear Schrödinger equation

In this paper, we examine the properties of hybrid solutions of the extended nonlinear Schrödinger equation. To begin with, we construct higher order positon/degenerate soliton solutions on the zero-intensity background by employing the generalized Darboux transformation method and investigate the interactions between smooth positons and multi-soliton solutions. We then construct another class of hybrid solutions with plane wave seed solution and investigate their dynamic interactions. More specifically, we scrutinize the interaction scenarios involving (i) one soliton with second order positon, (ii) two soliton with second order positon, (iii) one soliton with third order positon, (iv) second-order breather positon with breathers, and (v) third-order breather positon with breathers in the considered equation. By varying the nonlinear parameters that are present in the equation, we bring out a diverse range of intriguing behaviours in soliton-positon and breather-breather positon wave profiles.