Quasi-exact solvability, resonances and trivial monodromy in ordinary   differential equations
  A correspondence between the sextic anharmonic oscillator and a pair of third-order ordinary differential equations is used to investigate the phenomenon of quasi-exact solvability for eigenvalue problems involving differential operators with order greater than two. In particular, links with Bender-Dunne polynomials and resonances between independent solutions are observed for certain second-order cases, and extended to the higher-order problems. 
Patrick Dorey, Clare Dunning and Roberto Tateo
math-ph hep-th math.MP quant-ph