报告题目: A hierarchy of long wave-short wave type equations: quasi-periodic behavior of solutions and their representation

报告人：耿献国 教授，郑州大学

摘要:  Based on the Lenard recursion relation and the zero-curvature equation, we derive a hierarchy of long wave-short wave type equations associated with the 3x3 matrix spectral problem with three potentials. Resorting to the characteristic polynomial of the Lax matrix, a trigonal curve is defined, on which the Baker-Akhiezer function and two meromorphic functions are introduced. Analyzing some properties of the meromorphic functions, including asymptotic expansions at infinite points, we obtain the essential singularities and divisor of the Baker-Akhiezer function. Utilizing the theory of algebraic curves, quasi-periodic solutions for the entire hierarchy are finally derived in terms of the Riemann theta function.

时间： 6月1日（星期五）9:30—10:30

地点： 逸夫楼1417

报告邀请人：刘青平

报告题目: Inverse spectral transform for the Ragnisco-Tu equation with Heaviside initial condition

报告人：朱俊逸 教授，郑州大学

摘要:  The Ragnisco-Tu equation with the Heaviside initial condition is studied through the inverse spectral transform method. The procedure of regularization based is applied to construct the relation between potentials and dressing matrices. The explicit solutions are obtained and their dynamic behaviors are discussed.

时间： 6月1日（星期五）10:30—11:30

地点：逸夫楼1417

报告邀请人：刘青平

报告题目: Long-time asymptotics and modulational instability of the focusing Kundu-Eckhaus equation with nonzero boundary conditions

报告人：王灯山 教授，北京信息科技大学

摘要:  The long-time asymptotics of the focusing Kundu-Eckhaus equation with nonzero boundary conditions at infinity is investigated by the nonlinear steepest descent method of Deift and Zhou. Three asymptotic sectors in space-time plane are found: the plane wave sector I, plane wave sector II and an intermediate sector with a modulated one-phase elliptic wave. The asymptotic solutions of the three sectors are proposed by successively deforming the corresponding Riemann-Hilbert problems to solvable model problems. Moreover, a time-dependent g-function mechanism is introduced to remove the exponential growths of the jump matrices in the modulated one-phase elliptic wave sector. Finally, the modulational instability is studied to reveal the criterion for the existence of modulated elliptic waves in the central region.

时间： 6月4日（星期一） 15:30—16:30

地点： 逸夫楼1537

报告邀请人：田凯

报告题目: Cauchy two-matrix model, C-Toda lattice and CKP hierarchy

报告人：李春霞 副教授，首都师范大学

摘要:  Starting from the symmetric reduction in Cauchy biorthogonal polynomials, we derive the Toda equation of CKP type (C-Toda lattice) as well as its Lax pair by introducing time flows. Then, matrix integral solutions to the C-Toda lattice are extended to give solutions to the CKP hierarchy. It turns out that the time-dependent partition function of Cauchy two-matrix model is nothing but the \tau-function of the CKP hierarchy. In the end, the connection between the Cauchy two-matrix model and Bures ensemble is established from the viewpoint of integrable systems.

时间： 6月4日（星期一） 16:30—17:30

地点： 逸夫楼1537

报告邀请人：田凯