Quartic anharmonic many-body oscillator
  Two quantum quartic anharmonic many-body oscillators are introduced. One of them is the celebrated Calogero model (rational $A_n$ model) modified by quartic anharmonic two-body interactions which support the same symmetry as the Calogero model. Another model is the three-body Wolfes model (rational $G_2$ model) with quartic anharmonic interaction added which has the same symmetry as the Wolfes model. Both models are studied in the framework of algebraic perturbation theory and by the variational method. 
Alexander V. Turbiner