University of KashanMathematics Interdisciplinary Research2538-36396220210601Scaling Symmetry and a New Conservation Law of the Harry Dym Equation15115811150610.22052/mir.2021.240441.1270ENMehdi JafariDepartment of Mathematics, Payame Noor University, P. O. BOX 19395-3697, Tehran, Iran0000-0002-7154-7527Amirhesam ZaeimDepartment of Mathematics, Payame Noor University, P. O. BOX 19395-3697, Tehran, Iran0000-0001-9304-275XSomayesadat MahdionDepartment of Mathematics, Payame Noor University, P. O. BOX 19395-3697, Tehran, IranJournal Article20210120In 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.https://mir.kashanu.ac.ir/article_111506_624a8d3e8c7879cf5bab2580b9c13946.pdf