学术报告

题      目： Clarkson-McLeod solutions of the fourth Painlev\'e equation: Asymptotics and applications

报  告  人：赵育求   教授  (邀请人：黄志波 )

                                     中山大学

时      间：5月9日  16：00-17：00

地     点：数科院东楼401

报告人简介:

       赵育求，中山大学数学学院教授，博士生导师。研究方向为复分析与渐近分析。目前主要研究兴趣包括：Riemann-Hilbert方法及其应用，随机矩阵及其它数学物理问题，特殊函数与Painleve方程。在Constr. Approx., Comm. Math. Phys., Physica D, Proc. AMS,
Nonlinearity, Sci. China Math.等刊物发表论文60篇。

摘      要：

       Using the Deift-Zhou nonlinear steepest descent method, we derive the asymptotic behaviors for Clarkson-McLeod solutions of the fourth Painlev\'e equation at the negative infinity. This completes a proof of Clarkson and McLeod's conjecture on the asymptotics of this family of solutions. As applications, the total integrals of the Clarkson-McLeod solutions  and the  asymptotic approximations of the $\sigma$-form of  this family of solutions are also derived.