Abstract
Abstract
The Volterra lattice admits two non-Abelian analogs that preserve the integrability property. For each of them, the stationary equation for non-autonomous symmetries defines a constraint that is consistent with the lattice and leads to Painlevé-type equations. In the case of symmetries of low order, including the scaling and master-symmetry, this constraint can be reduced to second order equations. This gives rise to two non-Abelian generalizations for the discrete Painlevé equations and and for the continuous Painlevé equations P3, and P5.
Subject
General Physics and Astronomy,Mathematical Physics,Modeling and Simulation,Statistics and Probability,Statistical and Nonlinear Physics
Reference21 articles.
1. Generalized Matrix Form of the Inverse Scattering Method. In: Bullough R.K., Caudrey P.J. (eds) Solitons. Topics in Current Physics, vol 17 (Berlin: Springer);Wadati,1980
2. Darboux transformations for nonabelian and nonlocal equations of the Toda lattice type;Salle;Theor. Math. Phys.,1982
3. On the Painlevé test for non-Abelian equations;Balandin;Phys. Lett. A,1998
4. The isomonodromy approach in the theory of two-dimensional quantum gravitation;Its;Russ. Math. Surveys,1990
5. Discrete Painlevé equations and their appearance in quantum gravity;Fokas;Commun. Math. Phys.,1991
Cited by
8 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献