Nonlinear Stability of Periodic Travelling Wave Solutions for the Regularized Benjamin-Ono and BBM Equations
| dc.creator | Angulo, Jaime | |
| dc.creator | Scialom, Marcia | |
| dc.creator | Banquet, Carlos | |
| dc.date | 2009-04-29 | |
| dc.date.accessioned | 2026-07-07T13:09:57Z | |
| dc.date.available | 2026-07-07T13:09:57Z | |
| dc.description | This paper has various goals: first, we develop a local and global well-posedness theory for the regularized Benjamin-Ono equation in the periodic setting, second, we show that the Cauchy problem for this equation (in both periodic and non-periodic case) cannot be solved by an iteration scheme based on the Duhamel formula for negative Sobolev indices, third, a proof of the existence of a smooth curve of periodic travelling wave solutions, for the regularized Benjamin-Ono equation, with fixed minimal period 2L, is given. It is also shown that these solutions are nonlinearly stable in the energy space $H^{1/2}_{per}$ by perturbations of the same wavelength. Finally, an extension of the theory developed for the regularized Benjamin-Ono equation is given and as an example it is proved that the cnoidal wave solutions associated to the Benjamin-Bona-Mahony equation are nonlinearly stable in $H^1_{per}$. | |
| dc.identifier | https://arxiv.org/abs/0904.4623 | |
| dc.identifier | http://arxiv.org/abs/0904.4623 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/228912 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35Q53; 35B35 | |
| dc.title | Nonlinear Stability of Periodic Travelling Wave Solutions for the Regularized Benjamin-Ono and BBM Equations | |
| dc.type | text |