Journal
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
Volume 357, Issue 5, Pages 1753-1778Publisher
AMER MATHEMATICAL SOC
DOI: 10.1090/S0002-9947-04-03726-2
Keywords
integrable equation; soliton theory
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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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