Zhi-Qiang Li, Dmitry E. Pelinovsky, and Shou-Fu Tian
Exponential and algebraic double-soliton solutions of the massive Thirring model
Abstract:
The newly discovered exponential and algebraic double-soliton solutions of the massive Thirring model
in laboratory coordinates are placed in the context of the inverse scattering transform. We show that
the exponential double-solitons correspond to double isolated eigenvalues in the Lax spectrum, whereas
the algebraic double-solitons correspond to double embedded eigenvalues on the imaginary axis, where
the continuous spectrum resides. This resolves the long-standing conjecture that multiple embedded
eigenvalues may exist in the spectral problem associated with the massive Thirring model.
To obtain the exponential double-solitons, we solve the Riemann-Hilbert problem with the reflectionless potential
in the case of a quadruplet of double poles in each quadrant of the complex plane. To obtain the
algebraic double-solitons, we consider the singular limit where the quadruplet of double poles
degenerates into a symmetric pair of double embedded poles on the imaginary axis.
Keywords:
massive Thirring model; exponential solitons; algebraic solitons; double-pole solutions of Riemann-Hilbert problems,
isolated and embedded eigenvalues.