Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Solving the Korteweg-de Vries equation by its bilinear form: Wronskian solutions


Authors: Wen-Xiu Ma and Yuncheng You
Journal: Trans. Amer. Math. Soc. 357 (2005), 1753-1778
MSC (2000): Primary 35Q53, 37K10; Secondary 35Q51, 37K40
Published electronically: December 22, 2004
MathSciNet review: 2115075
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 35Q53, 37K10, 35Q51, 37K40

Retrieve articles in all journals with MSC (2000): 35Q53, 37K10, 35Q51, 37K40


Additional Information

Wen-Xiu Ma
Affiliation: Department of Mathematics, University of South Florida, Tampa, Florida 33620-5700
Email: mawx@math.usf.edu

Yuncheng You
Affiliation: Department of Mathematics, University of South Florida, Tampa, Florida 33620-5700
Email: you@math.usf.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-04-03726-2
PII: S 0002-9947(04)03726-2
Keywords: Integrable equation, soliton theory
Received by editor(s): June 2, 2003
Published electronically: December 22, 2004
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.