THE INVERSE SCATTERING TRANSFORM IN THE FORM OF A RIEMANN-HILBERT PROBLEM FOR THE DULLIN-GOTTWALD-HOLM EQUATION
| Autor: | Dmitry Shepelsky, Lech Zielinski |
|---|---|
| Přispěvatelé: | Zielinski, Lech |
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
Dullin-Gottwald-Holm equation
General Mathematics Mathematics::Analysis of PDEs [MATH] Mathematics [math] 01 natural sciences Omega symbols.namesake Riemann–Hilbert problem Dullin–Gottwald–Holm equation Initial value problem Camassa–Holm equation Boundary value problem 0101 mathematics Camassa-Holm equation inverse scattering trans- form Mathematical physics Mathematics Riemann-Hilbert problem Inverse scattering transform lcsh:T57-57.97 010102 general mathematics 010101 applied mathematics Formalism (philosophy of mathematics) Nonlinear Sciences::Exactly Solvable and Integrable Systems inverse scattering transform lcsh:Applied mathematics. Quantitative methods symbols |
| Zdroj: | Opuscula Mathematica, Vol 37, Iss 1, Pp 167-187 (2017) |
| 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: | OpenAIRE |
| Externí odkaz: |
|