Nonlocal integrable systems and covariant Hodograph transformations

报告题目:Nonlocal integrable systems and covariant Hodograph transformations

报告摘要:An integrable PT-symmetric system called nonlocal nonlinear Schrödinger (NLS) equation was proposed by Ablowitz and Musslimani [PRL-2013-No.064105]. It turns out that such nonlocal type integrable equations are derived from unreduced 2-component systems by using nonlocal reductions. In this talk we introduce a reduction approach to getting solutions of these nonlocal type integrable equations from the known solutions of those unreduced systems. Examples include semi-discrete NLS equation, and several nonlocal hierarchies with in the AKNS scheme. We also introduce other recent progress from other researchers such as formal transformation between local and nonlocal equations and reduction from matrix systems on half line.

We also introduce covariant hodograph transformations of nonlocal integrable systems. Short pulse (SP) equations serve as examples. First we describe connections between the first member in the AKNS negative hierarchy (AKNS(-1)) and several known integrable physical models, including Pedlosky's finite-amplitude baroclinic wave system, Konno-Oono system and its generalizations, SP equation and its complex and multi-component versions. These systems either are the AKNS(-1) system or can be derived from the system through suitable reductions and hodograph transformations. These connections can be extended to multi-component case. With this preparation we come to nonlocal reductions of the multi-component AKNS(-1) system and short pulse systems. In particular, we present nonlocal hodograph transformations between them.

时间:2018年5月11日(周五),13:30-15:00

地点:1C-324

报告人: 张大军教授(上海大学)

报告人简介:

张大军,男,1971年出生,博士,上海大学数学系教授,对离散可积系统的性质和精确解有深入研究。曾获上海市优秀博士学位论文,上海市高校优秀青年教师,主持多项国家自然科学基金面上项目。

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