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

Abstract

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 × 2 matrix Riemann-Hilbert problem in the complex plane. Further, one-cusp soliton solution is expressed in terms of the Riemann-Hilbert problem.

Keywords

Harry-Dym equation / Riemann-Hilbert problem / Initial-value problem / One-cusp soliton solution

References

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