<p>We have proposed wave modes physics to explain the power spectrum scaling in the magnetic presence of magnetic islands of the magnetopause. In the present manuscript, a model to study the role of waves in turbulence generation by taking the powerful whistler wave and weak KAW has been presented. The corresponding power spectrum, current sheet structures, and energy dissipation at magnetopause presence of magnetic islands are also analysed and discussed its relevance with observational data. This study is carried out numerically using the pseudospectral method here, space integration for spatial integrations and finite difference method for temporal integration have been used. To understand the physics behind the field localization, we developed a semianalytical model and got the development of electron and ion scale localization. Our study enhances the understanding of the role of wave-wave interaction physics in the presence of magnetic islands and the role of multi-scale physics in turbulence generation in space plasmas.</p>