Quasi-self-adjointness, conservation laws, and symmetry reductions with analytical solutions using Lie symmetry analysis and geometric approach for the (3+1)-dimensional generalized Bogoyavlensky-Konopelchenko equation

In this article, the (3 + 1)-dimensional generalized Bogoyavlensky-Konopelchenko equation has been examined for finding its exact closed form solitonic solutions with the help of symmetries. These symmetries are investigated by the means of the Lie symmetry approach, which is also known as classical Lie group method and geometric approach. In the geometric approach, the extended Harrison and Estabrook's differential forms have been used to investigate the infinitesimals of the generalized Bogoyavlensky-Konopelchenko equation. Moreover, by using formal Lagrangian, it is proved that the aforementioned partial differential equation satisfies the quasi-self-adjointness condition. Additionally, the conservation laws for the (3 + 1)-dimensional generalized Bogoyavlensky-Konopelchenko equation have been derived by imposing the "new conservation theorem, " which was proposed by Ibragimov. Finally, the exact closed form solutions are obtained with the help of Lie symmetries corresponding to the defined model.