INTEGRABLE NONLINEAR EVOLUTION-EQUATIONS AND DYNAMICAL-SYSTEMS IN MULTIDIMENSIONS

被引:4
作者
CALOGERO, F
机构
[1] IST NAZL FIS NUCL, ROME, ITALY
[2] UNIV ROME LA SAPIENZA 1, DIPARTIMENTO FIS, I-00185 ROME, ITALY
关键词
INTEGRABLE PDES; INTEGRABLE DYNAMICAL SYSTEMS; INTEGRABILITY IN MULTIDIMENSIONS;
D O I
10.1007/BF00994635
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The investigation of nonlinear evolution equations and dynamical systems integrable in multidimensions constitutes at present our main research interest. Here we survey findings obtained recently as well as over time: solvable equations (both PDEs and ODEs) are reported, philosophical motivations and methodological approaches are outlined. For more detailed treatments, including the display and analysis of solutions, the interested reader is referred to the original papers.
引用
收藏
页码:229 / 244
页数:16
相关论文
共 33 条
  • [1] Korteweg D.J., de Vries G., On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves, Philosophical Magazine Series 5, 39, pp. 422-443, (1895)
  • [2] Gardner C.S., Greene J.M., Kruskal M.D., Miura R. ML, Method for solving the Korteweg-de Vries equation, Phys. Rev. Lett., 19, pp. 1095-1097, (1967)
  • [3] Zakharov V.E., Shabat A.B., Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media, Soviet Physics JETP, 34, pp. 62-69, (1972)
  • [4] Ablowitz M.J., Kaup D.J., Newell A.C., Segur H., The inverse scattering transform-Fourier analysis for nonlinear problems, Stud. Appl. Math., 53, pp. 249-315, (1974)
  • [5] Zakharov V.E., Takhtadzjan L.A., Faddeev L.D., A complete description of the solution of the sine-Gordon equation, Soviet Phys. Dokl., 19, pp. 824-826, (1975)
  • [6] Lax P.D., Integrals of nonlinear equations of evolution and solitary waves, Communications on Pure and Applied Mathematics, 21, pp. 467-490, (1968)
  • [7] Toda M., Vibration of a chain with nonlinear interaction, J. Phys. Soc. Japan, 29, pp. 431-436, (1967)
  • [8] Toda M., Waves in nonlinear lattice, Progress of Theoretical Physics Supplement, 45, pp. 174-200, (1970)
  • [9] Calogero F., Solution of the one-dimensional N-body problem with quadratic and/or inversely-quadratic pair potentials, J. Math. Phys., 12, pp. 419-436, (1971)
  • [10] Flaschka H., The Toda lattice. I and II, Phys. Rev., 9 B, pp. 1924-1925, (1974)