N-double-pole solutions and asymptotic analysis for the massive thirring model in laboratory coordinates via the Riemann–Hilbert method

In this paper, the N-double-pole solutions for massive Thirring model (MTM) in laboratory coordinates are analyzed by utilizing the Riemann–Hilbert (RH) method. Given that the scattering coefficients possess double zeros, the inverse problems are formulated with the corresponding RH problems and reconstruction formulas, and the associated trace formulas are derived as well. Further, the N-double-pole solutions for the MTM system in the reflectionless case are explicitly derived in the form of determinants. Then, through an improved asymptotic analysis method that relies on the balance between exponential and algebraic parts, we deduce the explicit asymptotic solitons for single double-pole solutions. Moreover, the interaction properties of single double-pole solutions are analyzed including the phase shifts, relative distance and interaction force. It’s found that the asymptotic solitons are situated along the logarithmical trajectories and have the varying velocities with the rate [Formula: see text]. In addition, the soliton interactions in the two-component system are elastic and only the position shifts happen after the interaction.