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Conserved quantities for compressional dispersive Alfvén and soliton dynamics with non-local nonlinearity

The scaling invariance technique has been used to get the conserved quantities of (1+1)-dimensional dynamics of modulated compressional dispersive Alfvén (MCDA) and soliton dynamics with non-local nonlinearity. Conserved densities and their respective conserved fluxes are obtained by using the Euler and Homotopy operators. The conserved densities along with corresponding conserved fluxes lead towards the extraction of conservation laws.