On the Rosenau equation: Lie symmetries, periodic solutions and solitary wave dynamics

In this paper, we first consider the Rosenau equation with quadratic nonlinearity and identify its Lie symmetry algebra. We obtain reductions of to ODEs, find periodic analytical solutions in terms elliptic functions. Then, considering a general power-type nonlinearity, prove non-existence solitary waves for some parameters using Pohozaev type identities. The Fourier pseudo-spectral method is proposed single power nonlinearity. order investigate wave dynamics, generate initial profile by Petviashvili’s method. Then evolution overtaking collision are investigated various numerical experiments.