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2009, 2009(Special): 506-515. doi: 10.3934/proc.2009.2009.506

Wronskian solutions to integrable equations

Wen-Xiu Ma 1,

1. 

Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700, United States

Received  July 2008 Revised  March 2009 Published  September 2009

Wronskian determinants are used to construct exact solution to integrable equations. The crucial steps are to apply Hirota's bilinear forms and explore linear conditions to guarantee the Plücker relations. Upon solving the linear conditions, the resulting Wronskian formulations bring solution formulas, which can yield solitons, negatons, positions and complexitons. The solution process is illustrated by the Korteweg-de Vries equation and applied to the Boussinesq equation.
Keywords: complexiton, positon, Wronskian formulation, Hirota's bilinear equation, negaton, soliton.
Mathematics Subject Classification: Primary: 37K10, 35Q51; Secondary: 35Q53, 35Q55.
Citation: Wen-Xiu Ma. Wronskian solutions to integrable equations. Conference Publications, 2009, 2009 (Special) : 506-515. doi: 10.3934/proc.2009.2009.506
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