Irregular modulation of non-linear Alfvén/Beltrami wave coupled with an ion-sound wave.

Highlights: [•] A singularity of a system of differential equations may produce intrinsic solutions. [•] In the recently formulated non-linear model of Alfvén wave, we find a singularity. [•] The singularity produces an irregular modulation with an arbitrary number of pulses. [•] This occurs only to a fully non-linear Alfvén wave inherited from the Hall MHD. [•] Previous models that linearize the Hall term overlooked such a phenomenon. [ABSTRACT FROM AUTHOR]