N-soliton solutions and asymptotic analysis for the massive Thirring model in laboratory coordinates via the Riemann–Hilbert approach

In this paper, the N-soliton solutions for the massive Thirring model (MTM) in laboratory coordinates are analyzed via the Riemann–Hilbert (RH) approach. The direct scattering including the analyticity, symmetries, and asymptotic behaviors of the Jost solutions as ∣λ∣ → ∞ and λ → 0 are given. Considering that the scattering coefficients have simple zeros, the matrix RH problem, reconstruction formulas and corresponding trace formulas are also derived. Further, the N-soliton solutions in the reflectionless case are obtained explicitly in the form of determinants. The propagation characteristics of one-soliton solutions and interaction properties of two-soliton solutions are discussed. In particular, the asymptotic expressions of two-soliton solutions as ∣t∣ → ∞ are obtained, which show that the velocities and amplitudes of the asymptotic solitons do not change before and after interaction except the position shifts. In addition, three types of bounded states for two-soliton solutions are presented with certain parametric conditions.