Complexiton and interaction solutions to a specific form of extended Calogero–Bogoyavlenskii–Schiff equation via its bilinear form

Abstract In this article, we are focusing on an extended Calogero–Bogoyavlenskii–Schiff equation which was altered originally from a new generalized fourth-order nonlinear differential equation that obtained from Calogero–Bogoyavlenskii–Schiff equation. We apply simplified Hirota method, which is an exclusive form of the direct Hirota bilinear method, to a specific form of a new generalized fourth-order nonlinear differential equation. The key point in applicability of referred method is attainability proper forms of dispersion relations and phase shifts. Through this procedure, we present different types of solutions for three different cases. We also give constrictions for each solution type in this work so that readers can distinguish differences among types of solutions. In addition, we introduce some graphical representations for obtained solutions, even for existence of complexiton and interaction solutions.