An invariance analysis of the Vakhnenko–Parkes Equation

Lie symmetry analysis of differential equations is an effective technique to compute exact solutions of a differential equation, to reduce number of independent variables or to reduce the order and nonlinearity of the equation. The present article focuses on the symmetry analysis of Vakhnenko–Parkes Equation (VP Equation). At first, Lie point symmetries of the VP Equation that permit an optimal system of one-dimensional subalgebras are discussed and then using the commutator table we construct the discrete symmetries of the VP Equation using the modified Hydon’s method. Also, we compute the exact solutions using symmetry transformations. •We construct symmetries and first integrals of the Vakhnenko–Parkes equation.•Perform reductions.•Present graphs of the solitons.