This investigation presents the nonlinear interplay between pump wave (Kinetic Alfvén Wave (KAW)) and low-frequency ion acoustic wave (IAW) in the magnetized plasma. The model is developed by taking into account the ponderomotive nonlinearity associated due to the pump KAW. The coupled dimensionless equations (pump and IAW) are solved by adopting numerical simulation technique. The deduced results give the localization and filamentary structures of KAW, which eventually become chaotic with the evolution of time. The fundamental physics governing the dynamics of these two waves is influenced by the plasma beta () parameter; thereby affecting the nature of nonlinearity, dispersive properties and magnetic field amplification. The saturated spectra are analogous to that observed for many astrophysical scenarios for low (Chatterjee et al 2017 Nat. Commun.8 15970) and high beta (White et al 2019 Nat. Commun.10 1758; Tzeferacos et al 2017 Phys. Plasmas24 041404) plasma. This theoretical model outlining the nonlinear interaction can be imperative in understanding the dynamics of magnetic field amplification in various astrophysical scenarios.