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Exact solutions of equal-width equation and its conservation laws

Abstract In this work we investigate the equal-width equation, which is used for simulation of (1-D) wave propagation in non-linear medium with dispersion process. Firstly, Lie symmetries are determined and then used to establish an optimal system of one-dimensional subalgebras. Thereafter with its aid we perform symmetry reductions and compute new invariant solutions, which are snoidal and cnoidal waves. Additionally, the conservation laws for the aforementioned equation are established by invoking multiplier method and Noether’s theorem.