Baleanu, DumitruAlshomrani, Ali SalehUllah, Malik Zaka2022-02-242022-02-242021Baleanu, Dumitru; Alshomrani, Ali Saleh; Ullah, Malik Zaka (2021). "A new fourth-order integrable nonlinear equation: breather, rogue waves, other lump interaction phenomena, and conservation laws", Advances in Difference Equations, Vol. 2021, No. 1.1687-1839http://hdl.handle.net/20.500.12416/5049In this study, we investigate a new fourth-order integrable nonlinear equation. Firstly, by means of the efficient Hirota bilinear approach, we establish novel types of solutions which include breather, rogue, and three-wave solutions. Secondly, with the aid of Lie symmetry method, we report the invariance properties of the studied equation such as the group of transformations, commutator and adjoint representation tables. A differential substitution is found by nonlinear self-adjointness (NSA) and thereafter the associated conservation laws are established. We show some dynamical characteristics of the obtained solutions through via the 3-dimensional and contour graphs.eninfo:eu-repo/semantics/openAccessFourth-Order Integrable Nonlinear EquationLump SolutionsInteraction SolutionsInvariant AnalysisConservation LawsArticle2021110.1186/s13662-021-03352-6