TY - JOUR
T1 - Painlevé property and integrability
AU - Ercolani, Nicholas
AU - Siggia, Eric D.
N1 - Funding Information:
Rand, and J. Sethna for helpful remarks. The integrals for KdV were provided by Flaschka. Our research was supportedby the Department ofEnergy (Grant No. HDE-ACO2-83-ER), the National Science Foundation (Grant Nos. DMR-83 14625 and DMS-84 14092) and the Institute for Theoretical Physics in Santa Barbara.
PY - 1986/12/8
Y1 - 1986/12/8
N2 - For an n degree of freedom hyperelliptic separable hamiltonian, the pole series with n+1 free constants, through the Hamilton-Jacobi equation, bounds the degrees of the n-polynomials in involution. When all the pole series have no fewer than 2n constants, the phase space is conjectured to be just the direct product of 2n complex lines cut out by (2n-1) integrals.
AB - For an n degree of freedom hyperelliptic separable hamiltonian, the pole series with n+1 free constants, through the Hamilton-Jacobi equation, bounds the degrees of the n-polynomials in involution. When all the pole series have no fewer than 2n constants, the phase space is conjectured to be just the direct product of 2n complex lines cut out by (2n-1) integrals.
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U2 - 10.1016/0375-9601(86)90426-3
DO - 10.1016/0375-9601(86)90426-3
M3 - Article
AN - SCOPUS:0010054584
VL - 119
SP - 112
EP - 116
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
SN - 0375-9601
IS - 3
ER -