A simple and direct method for generating travelling wave solutions for nonlinear equations

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dc.creatorBazeia, D.
dc.creatorDas, Ashok
dc.creatorLosano, L.
dc.creatorSilva, A.
dc.date2007-03-19
dc.date2007-10-17
dc.date.accessioned2026-07-07T11:44:16Z
dc.date.available2026-07-07T11:44:16Z
dc.descriptionWe propose a simple and direct method for generating travelling wave solutions for nonlinear integrable equations. We illustrate how nontrivial solutions for the KdV, the mKdV and the Boussinesq equations can be obtained from simple solutions of linear equations. We describe how using this method, a soliton solution of the KdV equation can yield soliton solutions for the mKdV as well as the Boussinesq equations. Similarly, starting with cnoidal solutions of the KdV equation, we can obtain the corresponding solutions for the mKdV as well as the Boussinesq equations. Simple solutions of linear equations can also lead to cnoidal solutions of nonlinear systems. Finally, we propose and solve some new families of KdV equations and show how soliton solutions are also obtained for the higher order equations of the KdV hierarchy using this method.
dc.descriptionRevTex, 15 pages, 3 figures; version with new section and references, to appear in Annals of Physics
dc.identifierhttps://arxiv.org/abs/nlin/0703035
dc.identifierhttp://arxiv.org/abs/nlin/0703035
dc.identifierAnnalsPhys.323:1150-1167,2008
dc.identifierdoi:10.1016/j.aop.2007.10.003
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/201545
dc.subjectExactly Solvable and Integrable Systems
dc.subjectHigh Energy Physics - Theory
dc.subjectPattern Formation and Solitons
dc.titleA simple and direct method for generating travelling wave solutions for nonlinear equations
dc.typetext

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