References
- P. Basarab-Horwath, Integrability by quadratures for systems of involutive vector fields, Ukrain. Math. J. 43 (1991) 1236–1242.
- M.A. Barco and G.E. Prince, Solvable symmetry structures in differential form applications, Acta Appl. Math. 66 (2001) 89–121.
- L. Bianchi, Sugli spazi a tre dimensioni che ammettono un gruppo continuo di movimenti, Memorie di Matematica e di Fisica della Societa Italiana delle Scienze, Serie Terza Tomo XI (1898) 267–352 ( Reprint: Gen. Rel. Grav. 33 (2001) No 12).
- G. W. Bluman and S. C. Anco, Symmetry and Integration Methods for Differential Equations (Springer, Berlin, 2002).
- G. W. Bluman and G. J. Reid, New symmetries for ordinary differential equations, IMA J. Appl. Math. 40 (1988) 87–94.
- D. Catalano Ferraioli, Nonlocal aspects of λ-symmetries and ODEs reduction, J. Phys. A: Math Theor 40 (2007) 5479–5489.
- D. Catalano Ferraioli and P. Morando, Local and nonlocal solvable structures in the reduction of ODEs, J. Phys. A: Math Theor42 (2009) 035210 (15pp).
- D. Catalano Ferraioli and P. Morando, Applications of solvable structures to the nonlocal symmetry-reduction of ODEs, J. Nonlin. Math. Phys. 16 (2009) 27–42.
- M.E. Fels, Integrating scalar ordinary differential equations with symmetry revisited, Found. Comput. Math. 7 (2007) 417–454.
- G. Gaeta, Nonlinear symmetries and nonlinear equations (Kluwer, Dordrecht, 1994).
- G. Gaeta and P. Morando, On the geometry of lambda-symmetries and PDEs reduction, J. Phys. A: Math. Gen. 37 (2004) 6955–6975.
- M.L. Gandarias, E. Medina and C. Muriel, New symmetry reductions for some ordinary differential equations, J. Nonlin. Math. Phys. 9 (2002) 47–58.
- T. Hartl and C. Athorne, Solvable structures and hidden symmetries, J. Phys. A: Math Gen 27 (1994) 3463–3471.
- O. Krupkova, The geometry of Ordinary Variational Equations, Lect. Notes Math. 1678 (Springer, Berlin, 1997).
- C. Muriel and J.L. Romero, New method of reduction for ordinary differential equations, IMA J. Appl. Math. 66 (2001) 111–125.
- C. Muriel, J.L. Romero and P.J. Olver, Variational C∞-symmetries and Euler-Lagrange equations, J. Diff. Eq. 222 (2006) 164–184.
- P.J. Olver Application of Lie groups to differential equations (Springer, Berlin, 1993).
- E. Pucci and G. Saccomandi, On the reduction methods for ordinary differential equations, J. Phys. A: Math. Gen. 35 (2002) 6145–6155.
- J. Sherring and G. Prince, Geometric aspects of reduction of order, Trans. Amer. Math. Soc. 334 (1992) 433–453.
- A. M. Vinogradov et al. Symmetries and conservation laws for differential equations of mathematical physics (American Mathematical Society, Providence, 1999).