论文信息 - Invariant Painlevé analysis of partial differential equations

Invariant Painlevé analysis of partial differential equations

Abstract The whole Painleve analysis of PDEs is shown to be invariant under an arbitrary homographic transformation of the function ϕ defining the singularity manifold. The best expansion function is ϰ = ( ϕ x ϕ − ϕ xx 2ϕ x ) -1 . This solves the ques tion of invariance under the Mobius group in Painleve analysis and explains naturally Backlund transformation between solutions.

Robert Conte | R. Conte

[1] T. Miwa,et al. Painlevé test for the self-dual Yang-Mills equation , 1982 .

[2] A. Fordy,et al. Integrable nonlinear Klein-Gordon equations and Toda lattices , 1980 .

[3] Michael Tabor,et al. Analytic structure of the Lorenz system , 1981 .

[4] R. Conte,et al. Painleve analysis and Backlund transformation in the Kuramoto-Sivashinsky equation , 1989 .

[5] A. Mikhailov,et al. The reduction problem and the inverse scattering method , 1981 .

[6] R. Conte. Universal invariance properties of Painlevé analysis and Bäcklund transformation in nonlinear partial differential equations , 1988 .

[7] M. Tabor,et al. Integrating the nonintegrable: analytic structure of the Lorenz system revisited , 1988 .

[8] M. Tabor,et al. The Painlevé property for partial differential equations , 1983 .

[9] M. Ablowitz,et al. A connection between nonlinear evolution equations and ordinary differential equations of P‐type. II , 1980 .

[10] E. L. Ince. Ordinary differential equations , 1927 .

[11] J. Weiss. Bäcklund transformation and the Painlevé property , 1986 .

[12] J. Weiss,et al. The sine‐Gordon equations: Complete and partial integrability , 1984 .

[13] E. Hille,et al. Ordinary di?erential equations in the complex domain , 1976 .