Notes on the exact solutions and singularities of an X-point collapse in Hall magnetohydrodynamics

Abstract

A recent paper by A.~Z.~Janda [J.~Math.~Phys.~{\bf 59}, 061509 (2018)] presented a partial solution of the equations of dissipationless Hall magnetohydrodynamics (MHD) in terms of the Weierstrass elliptic function. Unfortunately, an error crept up in the analysis, where the kinetic and potential energies of the initial Hall MHD state were misidentified. The present comment presents the correct energy analysis and offers a complete solution of dissipationless Hall magnetohydrodynamics in terms of the Jacobi elliptic functions.Comment: 4 pages, 3 figure