The KP Hierarchy and Aspects of the Painleve Property : General and Mathematical Physics

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概要

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• We are concerned with the conjecture that the Painleve property is a necessary condition for the integrability of nonlinear equations. Following a suggestion by literatures (1) D. V. Chudnovsky, G. V. Chudnovsky and M. Tabor, Phys. Lett. 97A(1983), 268, and 2) A. K. Pogrebkov, Inverse Problems 5(1989), L7), our investigations will be based on the Lax-pair which we use in Sato's sense (3) E. Date, M. Jimbo, M. Kashiwara and T. Miwa in Nonlinear Integrable Systems-Classical and Quantum Theory, ed. M. Jimbo and T. Miwa (World Scientific, Singapore, 1983), p. 39, 4) M. Jimbo and T. Miwa, Publ. RIMS, Kyoto Univ. 19 (1983), 943, 5) Y. Ohta, J. Satsuma, D. Takahashi and T. Tokihiro, Prog. Theor. Phys. Suppl. No.94 (1988), 210). Leading orders, branch points and resonances are described for the Zakharov-Shabat equations of the KP-hierarchy.The symbolic manipulation system REDUCE, in particular its factorization algorithm for polynomials, is employed for finding the resonances. It is shown that the Painleve structures of various nonlinear equations, which have been discussed a lot in the literature, follow from our results.

• 理論物理学刊行会の論文
• 1990-12-25

著者

• Strampp Walter

  Fachbereich 17 Mathematik Gesamthochschule Kassel

• Strampp Walter

  Fachbereich 17-mathematik Gh-universitaet Kassel

• LANGER Christian

  Fachbereich 17-Mathematik, GH-Universitaet Kassel

• Langer Christian

  Fachbereich 17-mathematik Gh-universitaet Kassel

• STRAMPP Walter

  Department of Applied Physics, Faculty of Engineering University of Tokyo

• Strampp W.

  Fachbereich 17-Mathematik, GH-Universitaet Kassel

関連論文

• On the Resonance Pattern of Integrable Equations: General and Mathematical Physics
• Symmetries and the Painleve Property : General and Mathematical Physics
• The KP Hierarchy and Aspects of the Painleve Property : General and Mathematical Physics
• Lax Formulation, Painleve Property and Recursion Operator for a Space-Dependent Burgers' Equation
• A Comment on Backlund Transformations Connected with the Strum-Liouville Operator
• A Nonlinear Derivative Schroedinger-Equation: Its Bi-Hamilton Structures, Their Inverses, Nonlocal Symmetries and Mastersymmetries
• Solutions to Non-Linear Reaction-Diffusion Equations in Two Space Dimensions
• Backlund Transformations and Recursion Operators via Symmetry

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