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Wronskian solutions to integrable equations

Pages: 506 - 515, Issue Special, September 2009

 Abstract        Full Text (168.7K)              

Wen-Xiu Ma - Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700, United States (email)

Abstract: 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 Pl├╝cker 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:  Wronskian formulation, Hirota's bilinear equation, soliton, negaton, positon, complexiton
Mathematics Subject Classification:  Primary: 37K10, 35Q51; Secondary: 35Q53, 35Q55

Received: July 2008;      Revised: March 2009;      Published: September 2009.