A Riemann-Hilbert Approach to the Harry-Dym Equation on the Line

In this paper, the authors consider the Harry-Dym equation on the line with decaying initial value. They construct the solution of the Harry-Dym equation via the solution of a 2 x 2 matrix Riemann-Hilbert problem in the complex plane. Further, one-cusp soliton solution is expressed in terms of the Riemann-Hilbert problem.