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

Wen-Xiu Ma and Yuncheng You
Transactions of the American Mathematical Society
Vol. 357, No. 5 (May, 2005), pp. 1753-1778
Stable URL: http://www.jstor.org/stable/3845133
Page Count: 26
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Solving the Korteweg-de Vries Equation by Its Bilinear Form: Wronskian Solutions
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Abstract

A 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.

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