Title 1: The Cauchy two-matrix model, C-Toda lattice and CKP hierarchy
Date: 2019.11.23 09:05-09:50
Place: School of Science Meeting Room 1st
Reporter: LI Chunxia
Abstract: In my talk, I will first give a brief review on some known results of the Cauchy bi-orthogonal polynomials. Starting from the symmetric reduction of Cauchy biorthogonal polynomials, we derive the Toda equation of CKP type (or the 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 which reveals the time-dependent partition function of the Cauchy two-matrix model is nothing but the Tau-function of the CKP hiearchy. At last, the connection between the Cauchy two-matrix model and Bures ensemble is established from the point of view of integrable systems.
Title 2: Rational solution of discrete integrable systems
Date: 2019.11.23 09:50-10:35
Place: School of Science Meeting Room 1st
Reporter: ZHANG Dajun
Abstract: Hirota-Miwa equation (also known as Hirota’s equation/discrete AKP equation) is one of general 3D discrete integrable equations. Tau function of this equation admits an algebraic form, composed of polynomials of discrete independent coordinates. In this talk I will discuss properties of such a tau function and its applications in constructing rational solutions of integrable quadrilateral equations (such as the Nijhoff-Quispel-Capel equation, equations in the Adler-Bobenko-Suris (ABS) list and some multi-quadratic ABS equations). The tau function obeys a bilinear superposition formula, which provides generalized Burchnall-Chaundy polynomials.
Title 3: On integrable and nonintegrable spatial discrete NLS-type equations
Date: 2019.11.23 10:50-11:35
Place: School of Science Meeting Room 1st
Reporter: ZHU Zuonong
Abstract: In this talk, we will focus on the topic on integrable and nonintegrable spatial discrete nonlinear Schrodinger-type equations, including integrable and nonintegrable spatial discrete NLS equations, integrable and nonintegrable spatial discrete Hirota equations, and integrable and nonintegrable spatial discrete nonlocal NLS equations. This talk is based on the joint works with L.Y. Ma, C.Q. Song, J.L. Ji and Z.W. Xu.
Title 4: Dbar method with applications to 1+1-dimensional integrable systems
Date: 2019.11.23 14:30-15:15
Place: School of Science Meeting Room 1st
Reporter: Fan Engui
Abstract: In this talk, we first introduce short history of inverse scattering theory, then compare difference and connections among inverse scattering transformation, Riemann-Hilbert approach and dbar method. At last, we provide some applications in 1+1-dimensional integrable systems.
Title 5: Binary Darboux transform method to the coupled Sasa-Satsuma equation
Date: 2019.11.23 15:15-16:00
Place: School of Science Meeting Room 1st
Reporter: ZHANG Haiqiang
Abstract: The binary Darboux transformation method is applied to the coupled Sasa-Satsuma equations, which can be used to describe the propagation dynamics of femtosecond vector solitons in the birefringent fibers with third-order dispersion, self-steepening, and stimulated Raman scattering higher-order effects. An N-fold iterative formula of the resulting binary Darboux transformation is presented in terms of the quasideterminants. Via the simplest case of this formula, a few of illustrative explicit solutions to the coupled Sasa-Satsuma equations are generated from vanishing and non-vanishing backgrounds, which include the breathers, single- and double-hump bright vector solitons, and anti-dark vector solitons.
