School of Mathematical & Statistical Sciences Faculty Publications

Rational Solutions for Algebraic Solitons in the Massive Thirring Model

Document Type

Article

Publication Date

10-17-2026

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 N2 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√).

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https://rdcu.be/83jguSJ6WCxa

Publication Title

Journal of Nonlinear Science

DOI

10.1007/s00332-026-10326-z

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