D.E. Pelinovsky and A. Saalmann
Inverse scattering for the massive Thirring model
Nonlinear Dispersive Partial Differential Equations and Inverse Scattering
(Editors: P. Miller, P. Perry, J.C. Saut, and C. Sulem),
Fields Institute Communications 83 (Springer, New York, NY), 497-528 (2019)
Abstract:
We consider the massive Thirring model in the laboratory coordinates and explain how the
inverse scattering transform can be developed with the Riemann-Hilbert approach. The key ingredient
of our method is to transform the corresponding spectral problem to the equivalent forms: one is
suitable for the spectral parameter at the origin and the other one is suitable for the spectral parameter
at infinity. Global solutions to the massive Thirring model are recovered from the reconstruction
formulae at the origin and at in nity.
Keywords:
massive Thirring model, Jost functions, inverse scattering transform, Riemann-Hilbert problem