Wronskian solutions to integrable equations

Wen-Xiu Ma

doi:10.3934/proc.2009.2009.506

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2009, Volume 2009: 506-515. Doi: 10.3934/proc.2009.2009.506 open access

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Wronskian solutions to integrable equations

Wen-Xiu Ma^1,

1.
Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700

Received: July 2008

Revised: March 2009

Published: September 2009

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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.

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Mathematics Subject Classification: Primary: 37K10, 35Q51; Secondary: 35Q53, 35Q55.

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