The effect of interactions on two systems of few bosons is investigated. The method used is the exact diagonalization of the Hamiltonian in second quantized form with an improved truncation of the N-boson Hilbert space. In the first case, the disorder-induced localization of few bosons interacting via a repulsive contact potential is studied through the analysis of the level-spacing statistics. In the second case, a system of bosons in a two-dimensional harmonic trap in the presence of Rashba-type spin-orbit coupling is investigated.The low-energy states of the repulsively interacting two-boson system are characterized by computing their angular momenta, energy contributions and spatial densities.
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