Initial-boundary value problems for integrable evolution equations with 3脳3 Lax pairs

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• 作者：Jonatan Lenells ; ^{Jonatan_Lenells@baylor.edu}
• 关键词：Integrable system ; Riemann&ndash ; Hilbert problem ; Inverse scattering ; Initial-boundary value problem
• 刊名：Physica D
• 出版年：2012
• 期刊代码：55_01672789
• 类别：ph
• 出版时间：15 April, 2012
• 卷：241
• 期：8
• 页码：857-875
• 文件大小：397 K

摘要

We present an approach for analyzing initial-boundary value problems for integrable equations whose Lax pairs involve 3脳3 matrices. Whereas initial value problems for integrable equations can be analyzed by means of the classical Inverse Scattering Transform (IST), the presence of a boundary presents new challenges. Over the last fifteen years, an extension of the IST formalism developed by Fokas and his collaborators has been successful in analyzing boundary value problems for several of the most important integrable equations with 2脳2 Lax pairs, such as the Korteweg-de Vries, the nonlinear Schr枚dinger, and the sine-Gordon equations. In this paper, we extend these ideas to the case of equations with Lax pairs involving 3脳3 matrices.