Quasi-point separation of variables for the Henon-Heiles system and a   system with quartic potential
  We examine the problem of integrability of two-dimensional Hamiltonian systems by means of separation of variables. The systematic approach to construction of the special non-pure coordinate separation of variables for certain natural two-dimensional Hamiltonians is presented. The relations with SUSY quantum mechanics are discussed. 
S. Rauch-Wojciechowski and A.V. Tsiganov