摘要: We present a physicist’s approach to integrability and its detection. Starting from specific examples we working definition of what is meant by “integrability”. The detector on which this whole course in based the “Painleve method” links integrable character (differential) system singularity structure solutions. Recent results discrete systems are also discussed here. They are, for major part, obtained through application “singularity confinement” that equivalent Painleve method. Foremost among these equations generalize domain transcendental functions introduced have so many interesting applications nonlinear physics.
springer.com
harvard.edu
springerlink.com参考文章(81)
R. Garnier, Sur des équations différentielles du troisième ordre dont l'intégrale générale est uniforme et sur une classe d'équations nouvelles d'ordre supérieur dont l'intégrale générale a ses points critiques fixes Annales scientifiques de l'École normale supérieure. ,vol. 29, pp. 1- 126 ,(1912) , 10.24033/ASENS.644
What Is Integrability Springer Berlin Heidelberg. ,(1991) , 10.1007/978-3-642-88703-1
E. Fermi, P Pasta, S Ulam, M Tsingou, STUDIES OF THE NONLINEAR PROBLEMS ,(1955) , 10.2172/4376203
Rodney J. Baxter, Exactly solved models in statistical mechanics ,(1982)
Mark J. Ablowitz, Harvey Segur, Exact Linearization of a Painlevé Transcendent Physical Review Letters. ,vol. 38, pp. 1103- 1106 ,(1977) , 10.1103/PHYSREVLETT.38.1103
A. Ramani, B. Grammaticos, J. Satsuma, Integrability of multidimensional discrete systems Physics Letters A. ,vol. 169, pp. 323- 328 ,(1992) , 10.1016/0375-9601(92)90235-E
Jean Chazy, Sur les équations différentielles du troisième ordre et d'ordre supérieur dont l'intégrale générale a ses points critiques fixes Acta Mathematica. ,vol. 34, pp. 317- 385 ,(1911) , 10.1007/BF02393131
B. Grammaticos, B. Dorizzi, Integrable discrete systems and numerical integrators Mathematics and Computers in Simulation. ,vol. 37, pp. 341- 352 ,(1994) , 10.1016/0378-4754(94)00023-9
T.C. Bountis, A. Ramani, B. Grammaticos, B. Dorizzi, On the complete and partial integrability of non-Hamiltonian systems Physica A: Statistical Mechanics and its Applications. ,vol. 128, pp. 268- 288 ,(1984) , 10.1016/0378-4371(84)90091-8
H. Yoshida, B. Grammaticos, A. Ramani, Painlevé resonances versus Kowalevski exponents: Some exact results on singularity structure and integrability of dynamical systems Acta Applicandae Mathematicae. ,vol. 8, pp. 75- 103 ,(1987) , 10.1007/BF00046688