| Autor: |
Dmitry Shepelsky, Lech Zielinski |
| Jazyk: |
angličtina |
| Rok vydání: |
2017 |
| Předmět: |
|
| Zdroj: |
Opuscula Mathematica, Vol 37, Iss 1, Pp 167-187 (2017) |
| Druh dokumentu: |
article |
| ISSN: |
1232-9274 |
| DOI: |
10.7494/OpMath.2017.37.1.167 |
| Popis: |
The Cauchy problem for the Dullin-Gottwald-Holm (DGH) equation \[u_t-\alpha^2 u_{xxt}+2\omega u_x +3uu_x+\gamma u_{xxx}=\alpha^2 (2u_x u_{xx} + uu_{xxx})\] with zero boundary conditions (as \(|x|\to\infty\)) 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. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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