Lie symmetries and conservation laws of the Hirota–Ramani equation

In this paper, Lie symmetry method is performed for the Hirota–Ramani (H–R) equation. We will find the symmetry group and optimal systems of Lie subalgebras. Furthermore, preliminary classification of its group invariant solutions, symmetry reduction and nonclassical symmetries are investigated. Finally conservation laws of the H–R equation are presented.

► We find classical and nonclassical symmetries of the Hirota–Ramani equation. ► Also, we have constructed the optimal system of one-dimensional subalgebras of the H–R equation. ► The latter, creates the preliminary classification of group invariant solutions. ► We find the conservation laws of the H–R equation from the multiplier method.