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Supervised Machine Learning (ML) models for solar flare prediction rely on accurate labels for a given input data set, commonly obtained from the GOES/XRS X-ray flare catalog. With increasing interest in utilizing ultraviolet (UV) and extreme ultraviolet (EUV) image data as input to these models, we seek to understand if flaring activity can be defined and quantified using EUV data alone. This would allow us to move away from the GOES single pixel measurement definition of flares and use the same data we use for flare prediction for label creation. In this work, we present a Solar Dynamics Observatory (SDO) Atmospheric Imaging Assembly (AIA)-based flare catalog covering flare of GOES X-ray magnitudes C, M and X from 2010 to 2017. We use active region (AR) cutouts of full disk AIA images to match the corresponding SDO/Helioseismic and Magnetic Imager (HMI) SHARPS (Space weather HMI Active Region Patches) that have been extensively used in ML flare prediction studies, thus allowing for labeling of AR number as well as flare magnitude and timing. Flare start, peak, and end times are defined using a peak-finding algorithm on AIA time series data obtained by summing the intensity across the AIA cutouts. An extremely randomized trees (ERT) regression model is used to map SDO/AIA flare magnitudes to GOES X-ray magnitude, achieving a low-variance regression. We find an accurate overlap on 85% of M/X flares between our resulting AIA catalog and the GOES flare catalog. However, we also discover a number of large flares unrecorded or mislabeled in the GOES catalog. 

The interaction of localised solitary waves with large-scale, time-varying dispersive mean flows subject to non-convex flux is studied in the framework of the modified Korteweg–de Vries (mKdV) equation, a canonical model for internal gravity wave propagation and potential vorticity fronts in stratified fluids. The effect of large amplitude, dynamically evolving mean flows on the propagation of localised waves – essentially ‘soliton steering’ by the mean flow – is considered. A recent theoretical and experimental study of this new type of dynamic soliton–mean flow interaction for convex flux has revealed two scenarios where the soliton either transmits through the varying mean flow or remains trapped inside it. In this paper, it is demonstrated that the presence of a non-convex cubic hydrodynamic flux introduces significant modifications to the scenarios for transmission and trapping. A reduced set of Whitham modulation equations is used to formulate a general mathematical framework for soliton–mean flow interaction with non-convex flux. Solitary wave trapping is stated in terms of crossing modulation characteristics. Non-convexity and positive dispersion – common for stratified fluids – imply the existence of localised, sharp transition fronts (kinks). Kinks play dual roles as a mean flow and a wave, imparting polarity reversal to solitons and dispersive mean flows, respectively. Numerical simulations of the mKdV equation agree with modulation theory predictions. The mathematical framework developed is general, not restricted to completely integrable equations like mKdV, enabling application beyond the mKdV setting to other fluid dynamic contexts subject to non-convex flux such as strongly nonlinear internal wave propagation that is prevalent in the ocean.