Algebraic Solitons in the Massive Thirring Model

Abstract

This thesis presents exact solutions describing dynamics of N identical algebraic solitons in the massive Thirring model. Each algebraic soliton corresponds to a simple embedded eigenvalue in the Kaup–Newell spectral problem and attains the maximal mass among solitary waves traveling with the same speed. In the case of N = 2 solitons, we use expressions for two exponential solitons and find a new solution in the singular limit for the algebraic double-soliton which corresponds to a double embedded eigenvalue. To systematically derive the rational solutions for N identical algebraic solitons for any N ≥ 1, we employ the double-Wronskian method, a determinant-based approach that generates solitons to Hirota’s bilinear equations. While traditional stability techniques fail for algebraic solitons due to their embedded spectral nature, the exact solutions obtained here suggest persistence of algebraic solitons under time evolution.