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dc.contributor.authorJohnson, Mathew A.
dc.date.accessioned2015-03-02T22:06:56Z
dc.date.available2015-03-02T22:06:56Z
dc.date.issued2009-11-18
dc.identifier.citationJohnson, 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.urihttp://hdl.handle.net/1808/16915
dc.descriptionThis is the published version, also available here: http://dx.doi.org/10.1137/090752249.en_US
dc.description.abstractIn 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.publisherSociety for Industrial and Applied Mathematicsen_US
dc.subjectgeneralized Korteweg-de Vries equationen_US
dc.subjectperiodic wavesen_US
dc.subjectorbital stabilityen_US
dc.titleNonlinear Stability of Periodic Traveling Wave Solutions of the Generalized Korteweg–de Vries Equation9en_US
dc.typeArticle
kusw.kuauthorJohnson, Mathew A.
kusw.kudepartmentMathematicsen_US
dc.identifier.doi10.1137/090752249
kusw.oaversionScholarly/refereed, publisher version
kusw.oapolicyThis item meets KU Open Access policy criteria.
dc.rights.accessrightsopenAccess


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