  Since their discovery by SDO/AIA in EUV, rapid (phase speeds of 1000 km/s),
quasi-periodic, fast-mode propagating wave trains (QFPs) have been observed
accompanying many solar flares. They typically propagate in funnel-like
structures associated with the expanding magnetic field topology of the active
regions (ARs). The waves provide information on the associated flare pulsations
and the magnetic structure through coronal seismology. The reported waves
usually originate from a single localized source associated with the flare.
Here, we report the first detection of counter-propagating QFPs associated with
two neighboring flares on 2013 May 22, apparently connected by large-scale,
trans-equatorial coronal loops. We present the first results of 3D MHD model of
counter-propagating QFPs an idealized bi-polar AR. We investigate the
excitation, propagation, nonlinearity, and interaction of the
counter-propagating waves for a range of key model parameters, such as the
properties of the sources and the background magnetic structure. In addition to
QFPs, we also find evidence of trapped fast (kink) and slow mode waves
associated with the event. We apply coronal seismology to determine the
magnetic field strength in an oscillating loop during the event. Our model
results are in qualitative agreement with the AIA-observed counter propagating
waves and are used to identify the various MHD wave modes associated with the
observed event providing insights into their linear and nonlinear interactions.
Our observations provide the first direct evidence of counter-propagating fast
magnetosonic waves that can potentially lead to turbulent cascade and carry
significant energy flux for coronal heating in low-corona magnetic structures.
