Inc, MustafaYusuf, AbdullahiAliyu, Aliyu IsaBaleanu, Dumitru2019-12-252025-09-182019-12-252025-09-182018Baleanu, Dumitru; Inc, Mustafa; Yusuf, Abdullahi; et al., "Optimal system, nonlinear self-adjointness and conservation laws for generalized shallow water wave equation", Open Physics, Vol. 16, No. 1, pp.364-370, (2018).2391-5471https://doi.org/10.1515/phys-2018-0049https://hdl.handle.net/20.500.12416/14053Yusuf, Abdullahi/0000-0002-8308-7943; Isa Aliyu, Aliyu/0000-0002-9756-7374In this article, the generalized shallow water wave (GSWW) equation is studied from the perspective of one dimensional optimal systems and their conservation laws (Cls). Some reduction and a new exact solution are obtained from known solutions to one dimensional optimal systems. Some of the solutions obtained involve expressions with Bessel function and Airy function [1-3]. The GSWW is a nonlinear self-adjoint (NSA) with the suitable differential substitution, Cls are constructed using the new conservation theorem.eninfo:eu-repo/semantics/openAccessGswwOptimal SystemClsInfinitesimal GeneratorsNsaArticle10.1515/phys-2018-00492-s2.0-85050464507