Darboux transformations for quasi-exactly solvable Hamiltonians
  We construct new quasi-exactly solvable one-dimensional potentials through Darboux transformations. Three directions are investigated:   Reducible and two types of irreducible second-order transformations. The irreducible transformations of the first type give singular intermediate potentials and the ones of the second type give complex-valued intermediate potentials while final potentials are meaningful in all cases.   These developments are illustrated on the so-called radial sextic oscillator. 
N. Debergh, Boris F. Samsonov, B. Van Den Bossche