Solving the Korteweg-de Vries Equation by Its Bilinear Form: Wronskian Solutions
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.
Keywords
Cite
@article{arxiv.nlin/0503001,
title = {Solving the Korteweg-de Vries Equation by Its Bilinear Form: Wronskian Solutions},
author = {Wen-Xiu Ma and Yuncheng You},
journal= {arXiv preprint arXiv:nlin/0503001},
year = {2007}
}
Comments
26 pages including 12 figures