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This paper retrieves different types of solutions such as [Formula: see text]-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 [Formula: see text]-shaped interaction with rogue and kink, we will also obtain the [Formula: see text]-shaped interaction with periodic and kink, periodic cross-rational solutions. At the end, we will express the graphical representation for our newly achieved solutions.

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