Lie symmetry analysis and conservation laws with soliton solutions to a nonlinear model related to chains of atoms

We present the Lie symmetry analysis for the famous nonlinear equation describing chains of atoms with long range interaction. We also study the conservation laws by computing the conserved density and their associated fluxes by applying the scaling invariance approach. We use the Euler and the homotopy operators for the computations of conserved density and their corresponding fluxes respectively. In addition to these, we use an auxiliary ordinary differential equation method namely sub-ODE scheme to obtain bell type, kink shape, Jacobi elliptic, hyperbolic and few other solitary wave solutions with some constraints. At the end, we discuss our results graphically in distinct dimensions.