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The inverse scattering transform in the form of a Riemann-Hilbert problem for the Dullin-Gottwald-Holm equation

Shepelsky D., Zielinski L.

Opuscula Mathematica

2017

Vol. 37, no. 1

167--187

The Cauchy problem for the Dullin-Gottwald-Holm (DGH) equation [formula] with zero boundary conditions (as [formula]) is treated by the Riemann-Hilbert approach to the inverse scattering transform method. The approach allows us to give a representation of the solution to the Cauchy problem, which can be efficiently used for further studying the properties of the solution, particularly, in studying its long-time behavior. Using the proposed formalism, smooth solitons as well as non-smooth cuspon solutions are presented.