Conservation laws, soliton solutions for modified Camassa-Holm equation and (2+1)-dimensional ZK-BBM equation

By using the multiplier approach, we construct the conservation laws and the corresponding conserved quantities for the modified Camassa-Holm equation and (2 + 1)-dimensional Zakharov-Kuznetsov-Benjamin-Bona-Mahoney equation for each multipliers. We also deduce the soliton solutions for the equations using semi-inverse variational principle. We give the discussion of the properties of the soliton waves obtained numerically via some figures and the physical interpretation to complete these studies. Finally, we compare the solutions obtained with other solutions obtained in previous papers to prove that the results in this paper cannot appear anywhere.