Bäcklund Transformations of MKdV and Painlevé Equations

Abstract

For $N\ge 3$ there are $S_N$ and $D_N$ actions on the space of solutions of the first nontrivial equation in the $SL(N)MKdVhierarchy,generalizingthetwo$Z_2$ actions on the space of solutions of the standard MKdV equation. These actions survive scaling reduction, and give rise to transformation groups for certain (systems of) ODEs, including the second, fourth and fifth Painlevé equations.

8 pages, plain tex

References in corpus (1)

• Unitary Matrix Models and 2D Quantum Gravity (Virasoro constraints modified)

Cited by in corpus (5)

• Higher time-derivative theories from space-time interchanged integrable field theories
• Gauge Symmetry Origin of Bäcklund Transformations for Painlevé Equations
• A Dynamical Systems Approach to The Fourth Painleve Equation
• On Hamiltonian Formalism for Dressing Chain Equations of Even Periodicity
• Extended symmetry of higher Painlevé equations of even periodicity and their rational solutions