Asymptotics of the Riemann–Hilbert problem for a magnetic reconnection model in plasma

For the Riemann–Hilbert problem in a singularly deformed domain, an asymptotic expansion is found that corresponds to the limit transition from Somov's magnetic reconnection model to Syrovatskii's one as the relative shock front length $\varrho$ tends to zero. It is shown that this passage to the limit corresponding to $\varrho\to0$ is performed with the preservation of the reverse current region, while the parameter determining magnetic field refraction on shock waves grows as $\varrho^{-1/2}$. Moreover, the correction term to the Syrovatskii field has the order of $\rho$ and decreases in an inverse proportion to the distance from the current configuration.