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
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