dc.contributor.author | Johnson, Mathew A. | |
dc.contributor.author | Zumbrun, Kevin | |
dc.date.accessioned | 2015-03-02T21:49:31Z | |
dc.date.available | 2015-03-02T21:49:31Z | |
dc.date.issued | 2010-10-21 | |
dc.identifier.citation | Johnson, Mathew A. & Zumbrun, Kevin. "Transverse Instability of Periodic Traveling Waves in the Generalized Kadomtsev–Petviashvili Equation." SIAM J. Math. Anal., 42(6), 2681–2702. (22 pages). http://dx.doi.org/10.1137/090770758. | en_US |
dc.identifier.uri | http://hdl.handle.net/1808/16914 | |
dc.description | This is the published version, also available here: http://dx.doi.org/10.1137/090770758. | en_US |
dc.description.abstract | In this paper, we investigate the spectral instability of periodic traveling wave solutions of the generalized Korteweg–de Vries equation to long wavelength transverse perturbations in the generalized Kadomtsev–Petviashvili equation. By analyzing high and low frequency limits of the appropriate periodic Evans function, we derive an orientation index which yields sufficient conditions for such an instability to occur. This index is geometric in nature and applies to arbitrary periodic traveling waves with minor smoothness and convexity assumptions on the nonlinearity. Using the integrable structure of the ordinary differential equation governing the traveling wave profiles, we are then able to calculate the resulting orientation index for the elliptic function solutions of the Korteweg–de Vries and modified Korteweg–de Vries equations. | en_US |
dc.publisher | Society for Industrial and Applied Mathematics | en_US |
dc.subject | transverse instability | en_US |
dc.subject | generalized Korteweg-de Vries equation | en_US |
dc.subject | periodic waves | en_US |
dc.subject | generalized Kadomtsev-Petviashvili equation | en_US |
dc.title | Transverse Instability of Periodic Traveling Waves in the Generalized Kadomtsev–Petviashvili Equation | en_US |
dc.type | Article | |
kusw.kuauthor | Johnson, Mathew A. | |
kusw.kudepartment | Mathematics | en_US |
dc.identifier.doi | 10.1137/090770758 | |
kusw.oaversion | Scholarly/refereed, publisher version | |
kusw.oapolicy | This item meets KU Open Access policy criteria. | |
dc.rights.accessrights | openAccess | |