dc.contributor.author | Johnson, Mathew A. | |
dc.date.accessioned | 2015-03-02T22:06:56Z | |
dc.date.available | 2015-03-02T22:06:56Z | |
dc.date.issued | 2009-11-18 | |
dc.identifier.citation | Johnson, Mathew A. "Nonlinear Stability of Periodic Traveling Wave Solutions of the Generalized Korteweg–de Vries Equation." SIAM J. Math. Anal., 41(5), 1921–1947. (27 pages). http://dx.doi.org/10.1137/090752249. | en_US |
dc.identifier.uri | http://hdl.handle.net/1808/16915 | |
dc.description | This is the published version, also available here: http://dx.doi.org/10.1137/090752249. | en_US |
dc.description.abstract | In this paper, we study the orbital stability for a four-parameter family of periodic stationary traveling wave solutions to the generalized Korteweg–de Vries equation $u_t=u_{xxx}+f(u)_x$. In particular, we derive sufficient conditions for such a solution to be orbitally stable in terms of the Hessian of the classical action of the corresponding traveling wave ordinary differential equation restricted to the manifold of periodic traveling wave solutions. We show this condition is equivalent to the solution being spectrally stable with respect to perturbations of the same period in the case when $f(u)=u^2$ (the Korteweg–de Vries equation) and in neighborhoods of the homoclinic and equilibrium solutions if $f(u)=u^{p+1}$ for some $p\geq1$. | en_US |
dc.publisher | Society for Industrial and Applied Mathematics | en_US |
dc.subject | generalized Korteweg-de Vries equation | en_US |
dc.subject | periodic waves | en_US |
dc.subject | orbital stability | en_US |
dc.title | Nonlinear Stability of Periodic Traveling Wave Solutions of the Generalized Korteweg–de Vries Equation9 | en_US |
dc.type | Article | |
kusw.kuauthor | Johnson, Mathew A. | |
kusw.kudepartment | Mathematics | en_US |
dc.identifier.doi | 10.1137/090752249 | |
kusw.oaversion | Scholarly/refereed, publisher version | |
kusw.oapolicy | This item meets KU Open Access policy criteria. | |
dc.rights.accessrights | openAccess | |