Title 1: A hierarchy of algebraic solitons in the massive Thirring model
Speaker: Prof. Dr. Dmitry E. Pelinovsky (McMaster University, Canada)
Time: May 14, 2026,15:30-16:30
Venue: Room 3A01, Building No. 37, Wushan Campus
Abstract:
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}).
Title 2: Characterization of elliptic solutions in the defocusing mKdV equation
Speaker: Prof. Dr. Dmitry E. Pelinovsky (McMaster University, Canada)
Time: May 15, 2026,9:30-10:30
Venue: Room 3A01, Building No. 37, Wushan Campus
Abstract:
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.
