A Riemann-Hilbert approach to the Harry-Dym equation on the line

Abstract

In this paper, we consider the Harry-Dym equation on the line with decaying initial value. The Fokas unified method is used to construct the solution of the Harry-Dym equation via a $2\times 2$ matrix Riemann Hilbert problem in the complex plane. Further, one-cups soltion solution is expressed in terms of solutions of the Riemann Hilbert problem.

17 pages