Solving the Korteweg-de Vries equation by its bilinear form: Wronskian solutions
Solving the Korteweg-de Vries equation by its bilinear form: Wronskian solutions
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DOI：
10.1090/s0002-9947-04-03726-2
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发表时间：
2004-12
影响因子：
1.3
通讯作者：
W. Ma;Y. You
中科院分区：
文献类型：
--
作者：
W. Ma;Y. You
提出了一组由线性偏微分方程组成的广泛的充分条件，这些条件保证了朗斯基行列式以双线性形式求解科特韦格 - 德弗里斯方程。对求解所得的二阶和三阶偏微分方程的线性系统进行了系统分析，并给出了其代表性系统的解公式。关键技术是在求解相关的非齐次偏微分方程时应用参数变易法。所得到的解公式为我们构建科特韦格 - 德弗里斯方程的现有解以及许多新解（包括有理解、孤子、正子、负子、呼吸子、复子以及相互作用解）提供了一种全面的方法。
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.