学术报告报告题目1: A hierarchy of algebraic solitons in the massive Thirring model
报 告 人: Prof. Dr. Dmitry E. Pelinovsky (McMaster University, Canada)
报告时间: 2026年 5月 14日（星期四）下午 15：30-16：30
报告地点: 37号楼3A01
报告题目2: Characterization of elliptic solutions in the defocusing mKdV equation
报 告 人: Prof. Dr. Dmitry E. Pelinovsky (McMaster University, Canada)
报告时间: 2026年 5月 15日（星期五）上午 9：30-10：30
报告地点: 37号楼3A01
邀 请 人: 凌黎明 教授
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数学学院
2026年5月11日
报告1摘要：
An algebraic soliton of the massive Thirring model (MTM) is expressed by the simplest rational solution of the MTM with the spatial decay of O(x^{-1}). The corresponding potential is related to a simple embedded eigenvalue in the Kaup-Newell spectral problem. This work focuses on the hierarchy of rational solutions of the MTM, in which the N-th member of the hierarchy describes a nonlinear superposition of N algebraic solitons with identical masses and corresponds to an embedded eigenvalue of algebraic multiplicity N. We show that the hierarchy of rational solutions can be constructed by using the double-Wronskian determinants. The novelty of this work is a rigorous proof that each solution is defined by a polynomial of degree N^2 with (2N) arbitrary parameters, which admits N(N-1)/2 poles in the upper half-plane and N(N+1)/2 poles in the lower half-plane. Assuming that the leading-order polynomials have exactly N real roots, we show that the N-th member of the hierarchy describes the slow scattering of N algebraic solitons on the time scale O(t^{1/2}).
报告2摘要：
Breathers on an elliptic wave background consist of nonlinear superpositions of a soliton and a periodic wave, both traveling with different wave speeds and interacting periodically in the space-time. For the defocusing modified Korteweg-de Vries (mKdV) equation, the construction of general breathers has been an open problem since the elliptic wave is related to the elliptic degeneration of the hyperelliptic solutions of genus two. We have found the new representation of eigenfunctions of the Lax operator associated with the elliptic wave, which enables us to solve this open problem and to construct two families of breathers with bright (elevation) and dark (depression) profiles.
报告人介绍：
Dmitry Pelinovsky is a Professor in the Department of Mathematics at McMaster University. His research mainly focuses on the analysis of PDEs, integrable systems, solitons and numerical computations. He has published more than 280 SCI papers in prestigious international journals such as Comm. Pure Appl. Math., Adv. Math., Commun. Math. Phys. and Phys. Rev. Lett, with an h-index of 47. He has also authored three monographs: Localization in Periodic Potentials, Numerical Mathematics, and Nonlinear Physical Systems. Currently, he serves as the Editor-in-Chief of Studies in Applied Mathematics, Deputy Editor of Physica D, and an editorial board member of Physical Review E and other academic journals.