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

• Autorzy: Shepelsky D. , Zielinski L.

Identyfikatory

DOI

10.7494/OpMath.2017.37.1.167

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Dullin-Gottwald-Holm equation; Camassa-Holm equation; inverse scattering transform; Riemann-Hilbert problem

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2017
• Tom: Vol. 37, no. 1
• Strony: 167--187
• Opis fizyczny: Bibliogr. 21 poz.

Twórcy

autor

Shepelsky D.

• Institute for Low Temperature Physics 47 Lenin Avenue, 61103 Kharkiv, Ukraine
• V.N. Karazin Kharkiv National University 4 Svobody Square, 61022 Kharkiv, Ukraine

autor

Zielinski L.

• LMPA, Universite du Littoral Cote d’Opale 50 rue F. Buisson, CS 80699, 62228 Calais, France

Bibliografia

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Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).