Use of optimal subalgebra for the analysis of Lie symmetry, symmetry reductions, invariant solutions and conservation laws of the (3 + 1)-dimensional extended Sakovich equation

Abstract

This paper investigates the [Formula: see text]-dimensional extended Sakovich equation, which represents an essential nonlinear scientific model in the field of ocean physics. The Lie symmetry analysis has been utilized for extracting the non-traveling wave solutions of the [Formula: see text]-dimensional extended Sakovich equation. These solutions are investigated through infinitesimal generators, which are obtained from Lie’s continuous group of transformations. As there are infinite possibilities for the linear combination of infinitesimal generators, so a one-dimensional optimal system of subalgebra has been established using Olver’s standard approach. Moreover, by considering the optimal system of subalgebra, the extended Sakovich equation is converted into a solvable nonlinear PDE through symmetry reductions. Finally, the conservation laws for the governing equation have been derived using Ibragimov’s generalized theorem and quasi-self-adjointness condition.