| Abstract: |
| We present an algebraic soliton of the massive Thirring model (MTM) as the simplest rational solution with spatial decay $\mathcal{O}(x^{-1})$; the corresponding potential relates to an embedded eigenvalue in the Kaup-Newell spectral problem. The hierarchy of rational solutions is studied: the $N$th member describes a nonlinear superposition of $N$ algebraic solitons of equal mass and corresponds to an embedded eigenvalue of algebraic multiplicity $N$. Using double-Wronskian determinants, we rigorously prove that each solution is defined by a polynomial of degree $N^2$ with $2N$ free parameters, admitting $\frac{N(N-1)}{2}$ poles in the upper half-plane and $\frac{N(N+1)}{2}$ in the lower half-plane. Numerical root analysis shows that the $N$th member describes the slow scattering of $N$ algebraic solitons on the time scale $\mathcal{O}(\sqrt{t})$. |
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