Scaling Symmetry and a New Conservation Law of the Harry Dym Equation

Abstract

In this paper, we obtain a new conservation law for the Harry Dym equation by using the scaling method. This method is algorithmic and based on variational calculus and linear algebra. In this method, the density of the conservation law is constructed by considering the scaling symmetry of the equation and the associated flux is obtained by the homotopy operator. This density-flux pair gives a conservation law for the equation. A conservation law of rank 7 is constructed for the Harry Dym equation.

Keywords

• harry dym equation
• conversation laws
• scaling symmetry
• homotopy operator