In this article, we study the novel KdV model which makes a significant contribution to the understanding of a variety of nonlinear occurrences of ion-acoustic waves in plasma and acoustic waves in harmonic crystals. Hirota bilinearization will be used to carry out the task via the proper transformations. For various polynomial functions, several soliton solution types, specifically kink and rogue wave solutions, will be examined. We also present a kink wave and rogue wave interaction solution. The discovered solutions will be illustrated graphically. The existing work is widely used to report a variety of fascinating physical occurrences in the domains of shallow-water waves, ion-acoustic waves in plasma and acoustic waves in harmonic crystals.