Nonlinear kinetic Alfvén waves in upper ionosphere and reductive perturbation method Shaukat Ali Shan, Shanza Arooj and H. Saleem Eur. Phys. J. Plus, 139 8 (2024) 732 Published online: 14 August 2024 DOI: 10.1140/epjp/s13360-024-05463-x