dc.contributor.author | Li, Bing | |
dc.contributor.author | Ohta, Masahito | |
dc.contributor.author | Wu, Yifei | |
dc.contributor.author | Xue, Jun | |
dc.date.accessioned | 2021-03-18T13:42:12Z | |
dc.date.available | 2021-03-18T13:42:12Z | |
dc.date.created | 2020-09-29T14:46:27Z | |
dc.date.issued | 2020 | |
dc.identifier.citation | SIAM Journal on Mathematical Analysis. 2020, 52 (4), 3192-3221. | en_US |
dc.identifier.issn | 0036-1410 | |
dc.identifier.uri | https://hdl.handle.net/11250/2734264 | |
dc.description.abstract | In this work, we consider the following generalized Boussinesq equation \begin{align*} \partial_{t}^2u-\partial_{x}^2u+\partial_{x}^2(\partial_{x}^2u+|u|^{p}u)=0,\qquad (t,x)\in\R\times \R, \end{align*} with $0<p<\infty$. This equation has the traveling wave solutions $\phi_\omega(x-\omega t)$, with the frequency $\omega\in (-1,1)$ and $\phi_\omega$ satisfying \begin{align*} -\partial_{xx}{\phi}_{\omega}+(1-{\omega^2}){\phi}_{\omega}-{\phi}_{\omega}^{p+1}=0. \end{align*} Bona and Sachs (1988) proved that the traveling wave $\phi_\omega(x-\omega t)$ is orbitally stable when $0<p<4,$ $\frac p4<\omega^2<1$. Liu (1993) proved the orbital instability under the conditions $0<p<4,$ $\omega^2<\frac p4$ or $p\ge 4,$ $\omega^2<1$. In this paper, we prove the orbital instability in the degenerate case $0<p<4,\omega^2=\frac p4$. | en_US |
dc.language.iso | eng | en_US |
dc.publisher | Society for Industrial and Applied Mathematics | en_US |
dc.title | Instability of the solitary waves for the generalized Boussinesq equations | en_US |
dc.type | Peer reviewed | en_US |
dc.type | Journal article | en_US |
dc.description.version | acceptedVersion | en_US |
dc.source.pagenumber | 3192-3221 | en_US |
dc.source.volume | 52 | en_US |
dc.source.journal | SIAM Journal on Mathematical Analysis | en_US |
dc.source.issue | 4 | en_US |
dc.identifier.doi | https://doi.org/10.1137/18M1199198 | |
dc.identifier.cristin | 1835003 | |
dc.relation.project | Norges forskningsråd: 250070 | en_US |
dc.description.localcode | © 2020. This is the authors' accepted and refereed manuscript to the article. The final authenticated version is available online at: http://dx.doi.org/https://doi.org/10.1137/18M1199198 | en_US |
cristin.ispublished | true | |
cristin.fulltext | postprint | |
cristin.qualitycode | 2 | |