Double cnoidal waves of the Korteweg-de Vries equation: A boundary value approach
dc.contributor.author | Haupt, Sue Ellen | en_US |
dc.contributor.author | Boyd, John P. | en_US |
dc.date.accessioned | 2006-04-10T14:44:00Z | |
dc.date.available | 2006-04-10T14:44:00Z | |
dc.date.issued | 1991-05 | en_US |
dc.identifier.citation | Haupt, Sue Ellen, Boyd, John P. (1991/05)."Double cnoidal waves of the Korteweg-de Vries equation: A boundary value approach." Physica D: Nonlinear Phenomena 50(1): 117-134. <http://hdl.handle.net/2027.42/29346> | en_US |
dc.identifier.uri | http://www.sciencedirect.com/science/article/B6TVK-46JYFGX-37/2/f4addc93751d72af7c3015c43331b9c2 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/29346 | |
dc.description.abstract | Double cnoidal waves of the Korteweg-de Vries equation are studied by direct solution of the nonlinear boundary value problems. These double cnoidal waves, which are the spatially periodic generalization of the well-known double soliton, are exact solutions with two independent phase speeds. The equation is written in terms of two phase variables and expanded in two-dimensional Fourier series. The small-amplitude solution is obtained via the Stokes' perturbation expansion. This solution is numerically extended to larger amplitude by employing a Newton-Kantorovich[+45 degree rule]continuation in amplitude[+45 degree rule] Galerkin algorithm. The crests of the finite amplitude solution closely match the sech2 solitary wave form and the three cases of solitary wave interaction described by Lax are identified for the double cnoidal waves. This simple approach reproduces specific features such as phase shift upon collision, distinction between instantaneous and average phase speeds, and a "paradox of wavenumbers". | en_US |
dc.format.extent | 1167126 bytes | |
dc.format.extent | 3118 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.language.iso | en_US | |
dc.publisher | Elsevier | en_US |
dc.title | Double cnoidal waves of the Korteweg-de Vries equation: A boundary value approach | en_US |
dc.type | Article | en_US |
dc.rights.robots | IndexNoFollow | en_US |
dc.subject.hlbsecondlevel | Physics | en_US |
dc.subject.hlbsecondlevel | Mathematics | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Department of Atmospheric, Oceanic, and Space Science, The University of Michigan, 2455 Hayward Avenue, Ann Arbor, MI 48109, USA | en_US |
dc.contributor.affiliationum | Department of Atmospheric, Oceanic, and Space Science, The University of Michigan, 2455 Hayward Avenue, Ann Arbor, MI 48109, USA | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/29346/1/0000414.pdf | en_US |
dc.identifier.doi | http://dx.doi.org/10.1016/0167-2789(91)90084-M | en_US |
dc.identifier.source | Physica D: Nonlinear Phenomena | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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