Modulational instability and mixed breather–lump interaction solutions in the (2+1)-dimensional KMN equation

Abstract

Under investigation is the (2[Formula: see text]+[Formula: see text]1)-dimensional KMN equation, which is a new extension of the well-known nonlinear Schrödinger equation. Firstly, we investigate the modulational instability (MI) of the plane wave states for this equation. Secondly, we explore several types of interesting mixed breather–lump solutions in orders [Formula: see text] and [Formula: see text] cases by using the generalized [Formula: see text]-fold Darboux transformation (DT). Moreover, we also provide the graphical analysis of such mixed interaction solutions to better understand their dynamical behavior. Finally, we sum up a few mathematical features to obtain special mixed interaction structures through the generalized [Formula: see text]-fold DT. The results obtained in this paper might excite the interest in nonlinear optics and relevant fields.