Abstract
This paper retrieves different types of solutions such as M-shaped rational solutions with one and two kinks, homoclinic breather, multi-waves, periodic cross-kink and kink-cross rational solutions for Radhakrishnan-Kundu-Lakshmanan equation (RKLE). We will study the M-shaped interaction with rogue and kink, we will also obtain the M-shaped interaction with periodic and kink, periodic cross-rational solutions. At the end, we will express the graphical representation for our newly achieved solutions.