Dym equation: group analysis and conservation laws

In this paper group-invariant properties of the Dym equation are studied. Lie symmetries are given and some group-invariant solutions are found with the use of similarity variables obtained from these operators. Conservation laws are computed via three methods. Direct method for construction of conservation laws is introduced by the concept of multipliers and Euler-Lagrange operator. Next, the non-linearly self-adjointness of the considered PDE is stated. Then, the modified Noether's theorem is used for finding conservation laws. Finally, the third method is established via the Hereman-Pole method by using the evolutionary form of the equation.