关于Korteweg de Vries型方程的Bäcklund变换的分解

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Decompositions of Bäcklund Transformations for the Korteweg-de Vries Equation

摘要: 本文讨论了Korteweg-de Vries(K-dV)方程,经修改的K-dV方程、高阶K-dV方程和柱面K-dV方程的scale变换和Bäcklund变换的分解,得出了B_a=S_a^-1B₁S_a型分解关系式.这对深入研究Bäcklund变换的内在结构,特别是对群结构性质极为有益的.

Abstract: In this paper, decomposition relations such B_a=S_a^-1B₁S_a, connecting scale transformations and Bäcklund transformations for the Korteweg-de Vries K-dV, modified K-dV, higher-order K-dV and cylindrical equations, are obtained.

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