Derivation and Implicit Solution of the Harry Dym Equation, and Its Connections with the Korteweg-De Vries Equation

摘要

THe Harry Dym equation, which is related to the classical string problem, is derived in three different ways. An implicit cusp solitary wave solution is constructed via a simple direct method. The existing connections between the Harry Dym and the Korteweg-de Vries equations are uniformised and simplified, and transformations between their respective solutions are carried out explicitly. Whenever possible, physical insights are provided. (kr)