The Painlevé property for partial differential equations

Journal of Mathematical Physics - Tập 24 Số 3 - Trang 522-526 - 1983
John Weiss1, M. Tabor2,1, G. F. Carnevale1
1Center for Studies of Nonlinear Dynamics, La Jolla Institute, La Jolla, California 92038
2Applied Mathematics, Committee on

Tóm tắt

In this paper we define the Painlevé property for partial differential equations and show how it determines, in a remarkably simple manner, the integrability, the Bäcklund transforms, the linearizing transforms, and the Lax pairs of three well-known partial differential equations (Burgers’ equation, KdV equation, and the modified KdV equation). This indicates that the Painlevé property may provide a unified description of integrable behavior in dynamical systems (ordinary and partial differential equations), while, at the same time, providing an efficient method for determining the integrability of particular systems.

Từ khóa


Tài liệu tham khảo

1890, Acta Math., 14, 81, 10.1007/BF02413316

1982, Analytic structure of the Henon-Heiles Hamiltonian in integrable and nonintegrable regimes, J. Math. Phys., 23, 531, 10.1063/1.525389

1982, Integrable Hamiltonian systems and the Painlevé property, Phys. Rev. A, 25, 1257, 10.1103/PhysRevA.25.1257

1980, J. Math. Phys., 21, 715, 10.1063/1.524491

1968, Integrals of Nonlinear Equations of Evolution and Solitary Waves, Commun. Pure Appl. Math., 21, 674

1974, Analytic Solutions of the Two-Dimensional Kortwegde Vries Equation, Pis’ma Zh. Eksp. Teor. Fiz., 19, 753

1974, JETP Lett., 19, 387

Thông tin
Thông tin xuất bản

Journal of Mathematical Physics

Tập 24 Số 3

522-526

Thông tin tác giả