Derivation and implicit solution of the Harry Dym equation and its connections with the Korteweg-de Vries equation
- 7 February 1989
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 22 (3) , 241-255
- https://doi.org/10.1088/0305-4470/22/3/009
Abstract
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.Keywords
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