Solving the Korteweg-de Vries Equation by Its Bilinear Form: Wronskian Solutions

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dc.creatorMa, Wen-Xiu
dc.creatorYou, Yuncheng
dc.date2005-03-01
dc.date.accessioned2026-07-07T05:36:19Z
dc.date.available2026-07-07T05:36:19Z
dc.descriptionA broad set of sufficient conditions consisting of systems of linear partial differential equations is presented which guarantees that the Wronskian determinant solves the Korteweg-de Vries equation in the bilinear form. A systematical analysis is made for solving the resultant linear systems of second-order and third-order partial differential equations, along with solution formulas for their representative systems. The key technique is to apply variation of parameters in solving the involved non-homogeneous partial differential equations. The obtained solution formulas provide us with a comprehensive approach to construct the existing solutions and many new solutions including rational solutions, solitons, positons, negatons, breathers, complexitons and interaction solutions of the Korteweg-de Vries equation.
dc.description26 pages including 12 figures
dc.identifierhttps://arxiv.org/abs/nlin/0503001
dc.identifierhttp://arxiv.org/abs/nlin/0503001
dc.identifierTrans. Amer. Math. Soc., 357 (2005), No.5, 1753-1778
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/80949
dc.subjectExactly Solvable and Integrable Systems
dc.subjectPattern Formation and Solitons
dc.titleSolving the Korteweg-de Vries Equation by Its Bilinear Form: Wronskian Solutions
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