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 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: Wronskian formulation, Hirota's bilinear equation,
soliton, negaton, positon, complexiton
Received: July 2008; Revised: March 2009; Published: September 2009.