Abstract
We present our study of kaonic three-body KNN , KNN and KKK and four-body KNNN , and KKNN clusters within the framework of a potential model using the method of hyperspherical functions in momentum representation. To perform a numerical calculations for the bound state energy of the light kaonic system, we use a set of different potentials for the nucleon-nucleon and KN interactions, as well as for the kaon-kaon interaction. The calculations show that a quasibound state energy is not sensitive to the NN interaction, and it shows very strong dependence on the KN potential. We also compare our results with those obtained using different theoretical approaches. The theoretical discrepancies in the binding energy and width for the lightest kaonic system related to the different NN and KN interactions are addressed.