报告人：冯宝峰 教授

所在单位：Department of Mathematics, University of Texas-Pan, American

主持人：陈勇 教授

报告人简介：

       冯宝峰教授，男，理学博士。1989年于清华大学获学士学位，1997年取得日本名古屋大学获硕士学位，2000年于日本京都大学获博士学位。美国德克萨斯大学数学系教授，在可积系统和离散的可积系统，偏微分方程科学计算和数值方法（PDE），非线性波，格点的形成和摄动方法等众多领域发表多篇学术论文。

报告1：A short wave model of the two-component Degasperis-Proceli equation

报告时间：2016年6月5日 9:00-11:00

报告地点：理科大楼B1102

报告摘要：

      In the present talk, we propose a short wave model of the two-component Degasperis-Proceli equation. First, we give a review on the bilinear equation of extended BKP hierarchy which derives the reduced Ostrovsky equation, or the short wave model of the Degasperis-Proceli equation by periodic 3 reduction. Starting from the same bilinear equation, we will show a two-component reduced Ostrovsky equation can be derived by a pseudo 3-reduction. As a byproduct, its N-soliton solution in terms of pfaffians are constructed. Furthermore, we give the Lax pair of the two-component reduced Ostrovsky equation to assure the integrability of the proposed equation.

报告2：Integrable semi-discretizations of a two-component reduced Ostrovsky equation

报告时间：2016年6月5日 15:00-17:00（最新更新）

报告地点：理科大楼B1102

报告摘要：

      Based on a two-component reduced Ostrovsky equation, or a short wave model of the two-component Degasperis-Proceli equation we recently proposed, we will show how to construct its integrable semi-discretization of this new model. We start with a modied BKP hierarchy, which is a Backlund transformation of the extended BKP hierarchy which gives the two-component reduced Ostrovsky equation, an integrable semi-discrete analogue of the two-component reduced Ostrovsky equation is constructed by dening an appropriate discrete hodograph transformation and dependent variable transformations. Meanwhile, its N-soliton solution in terms of pfaffian is also provided. Interestingly, the backward difference form of above semi-discrete two-component reduced Ostrovsky equation gives rise to the integrable semi-discretization of the short wave model of a two-component DP equation, which strongly implies the integrability of the two-component DP equation.