Title1: Tetragonal curves and algebro-geometric solutions to the Satsuma-Hirota coupled hierarchy
Speaker: Prof. Xianguo Geng ( Zhengzhou University )
Time: Thur, May.6 2021, PM: 15:00-16:00
Location: Tencent Conference
Meeting Number: 350 271 734
Title2: Some Applications of the steepest descent method to long-time asymptotics
Speaker: Prof. Bo Xue ( Zhengzhou University )
Time: Thur, May.6 2021, PM: 16:00-17:00
Location: Tencent Conference
Meeting Number: 350 271 734
Inviter: Prof. Liming Lin
Abstract1:
On the basis of the characteristic polynomials of Lax matrixes for the soliton hierarchies, we introduce the corresponding algebraic curves, including the hyperelliptic curve, trigonal curve, and tetragonal curve. We study the calculation of genus of algebraic curve, properties at infinity, and the construction of three kinds of Abel differentials. We establish the corresponding Baker-Akhiezer functions and meromorphic functions. The straightening out of various soliton flows is exactly given through the Abel map and Abel-Jacobi coordinates. Using the theory of algebraic curves, we obtain the explicit Riemann theta function representations of the Baker-Akhiezer function and the meromorphic function. As an illustration, we arrive at algebro-geometric solutions of the entire Satsuma-Hirota coupled hierarchy.
Abstract2:
The initial value problem for the Sasa–Satsuma equation is transformed to a 3×3 matrix Riemann–Hilbert problem with the help of the corresponding Lax pair. Two distinct factorizations of the jump matrix and a decomposition of the vector-valued function are given, from which the long-time asymptotics for the Sasa–Satsuma equation with decaying initial data is obtained by using the nonlinear steepest descent method .