On the symmetries of integrable systems. (English) Zbl 0816.35122
Fokas, A. S. (ed.) et al., Important developments in soliton theory. Berlin: Springer-Verlag. Springer Ser. Nonlinear Dyn. 283-301 (1993).
It is shown that the algebra of symmetries of a nonlinear evolution equation solvable by the inverse scattering transform method has a commutative part and a noncommutative one.
It is proved that all possible symmetries of the Kadomtsev-Petviashvili equation may be enumerated by collections of integers \((n, m)\). It is shown that the action of \((m, 1)\) symmetries on the finite-gap solutions of this equation corresponds to the action of the conformal algebra on Riemann surfaces.
For the entire collection see [Zbl 0801.00009].
It is proved that all possible symmetries of the Kadomtsev-Petviashvili equation may be enumerated by collections of integers \((n, m)\). It is shown that the action of \((m, 1)\) symmetries on the finite-gap solutions of this equation corresponds to the action of the conformal algebra on Riemann surfaces.
For the entire collection see [Zbl 0801.00009].
Reviewer: V.A.Yumaguzhin (Pereslavl’-Zalesskij)
MSC:
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 58J70 | Invariance and symmetry properties for PDEs on manifolds |
