Long time asymptotic系列课程
报告专家：翁为方（电子科技大学）
课程时间：
2024年11月5日（星期二）下午16：00-18：00
2024年11月8日（星期五）上午9：30-11：30
2024年11月12日（星期二）上午14：00-16：00
2024年11月15日（星期五）上午9：30-11：30
2024年11月19日（星期二）上午14：00-16：00
2024年11月22日（星期五）上午9：30-11：30
2024年11月29日（星期五）上午9：30-11：30
课程地点：国家天元数学西南中心518报告厅
课程摘要：
题目：Long time asymptotic behavior of the defocusing nonlinear Schrödinger equation-I
摘要：In this talk，we introduce long-time asymptotic behavior of the defocusing nonlinear Schrödinger (NLS) equation. We mainly introduce the inverse scattering transform of defocusing NLS equation.
题目：Long time asymptotic behavior of the defocusing nonlinear Schrödinger equation-II
摘要：In this talk，we introduce long-time asymptotic behavior of the defocusing (NLS) equation. We construct Riemann-Hilbert problem of defocusing NLS equation. Then we construct a function δ(z) and provide the first matrix transformation.
题目：Long time asymptotic behavior of the defocusing nonlinear Schrödinger equation-III
摘要：In this talk，we introduce long-time asymptotic behavior of the defocusing (NLS) equation. We introduce the dbar analysis to define extensions of the jump matrix for the non-linear steepest descent method.
题目：Long time asymptotic behavior of the defocusing nonlinear Schrödinger equation-I
摘要：In this talk，we introduce long-time asymptotic behavior of the focusing nonlinear Schrödinger (NLS) equation. We mainly introduce the inverse scattering transform of focusing NLS equation.
题目：Long time asymptotic behavior of the focusing nonlinear Schrödinger equation-II
摘要：In this talk，we introduce long-time asymptotic behavior of the focusing NLS equation. We construct Riemann-Hilbert problem of focusing NLS equation. Then we construct a meromorphic function T and provide the first matrix transformation.
题目：Long time asymptotic behavior of the focusing nonlinear Schrödinger equation-III
摘要：In this talk，we introduce long-time asymptotic behavior of the focusing NLS equation. We introduce the steepest descent analysis of Riemann-Hilbert problem. Then we construct a global model solution.
题目：Long-time asymptotic for the focusing nonlinear Schrodinger equation with step-like initial value
摘要：In this talk, we introduce the initial value problem for the focusing nonlinear Schrodinger equation with step-like initial data. We construct Riemann-Hilbert problem of focusing NLS equation with step-like initial data. We introduce the long-time asymptotics of the solution to this problem.
专家简介：
简介：翁为方，讲师，电子科技大学数学科学学院。2017年9月至2022年6月在中国科学院数学与系统科学研究院硕博连读。2022年7月至2024年7月在清华大学数学科学系做博士后。主要研究数学物理中的孤子理论与可积系统及其应用，已在国际重要的非线性科学领域的SCI 核心期刊Journal of Differential Equations、Physica D等发表了 15篇论文。
邀请人：李世豪
