Evolution of non-stationary quasi-periodic pulsations in solar flares with Aditya-L1/HEL1OS and GOES

In the present work, we use a phase-resolved methodology for the detection and characterization of non-stationary quasi-periodic pulsations (QPPs) in the hard X-ray light curves observed from the High Energy L1-Orbiting X-ray Spectrometer instrument on board the Aditya-L1 mission, complemented by cross-examination using soft X-ray observations from Geostationary Operational Environmental Satellites. Our approach combines variational mode decomposition with Hilbert-Huang analysis and wavelet transforms to sharpen transient QPP signatures, extract narrowband amplitude-frequency modulated modes and track instantaneous period drift across various phases of the flares. By applying these tools to pre-flare, impulsive and decay phases and associated intervals, we identify the timing, duration and evolution of statistically significant oscillations and assess their relation to thermal and non-thermal flare components. Finally, we extend the method to the catalogue of non-stationary QPP flares reported by Mehta et al. (Mehta et al. 2023 Mon. Not. R. Astron. Soc. 523, 3689-3698. (doi:10.1093/mnras/stad1619)), where we identify statistically significant QPPs in both impulsive and decay phases for 74 out of 98 flares. Among these, 56.8% exhibit small period drifts, while 43.2% show larger deviations. Positive period drift dominates (73%), indicating a systematic increase in characteristic timescales as flares evolve. A phase-period-duration analysis reveals distinct regimes of non-stationarity, including overlapping multi-mode oscillations, intermittent same-period episodes and strongly evolving multi-modal behaviour. This article is part of the theme issue 'Transferable mechanisms in the oscillatory processes of solar and stellar flares'.