Similarity Reductions for the Nonlinear Evolution Equation Arising in the Fermi-Pasta-Ulam Problem
-
摘要: 利用Clarkson和Kruskal引入的直接法和Lou的改进的直接法,给出了源于Fermi-Pasta-Ulam问题的非线性发展方程的4种类型的相似约化.Abstract: Four families of similarity reductions are obtained for the nonlinear evolution equation arising in the Fermi-Pasta-Ulam problem via using both the direct method due to Clarkson and Kruskal and the improved direct method due to Lou.
-
Key words:
- nonlinear evolution equation /
- FPU problem /
- similarity reduction
-
[1] Fermi E,Pasta J,Ulam S.Studies of Nonlinear Problems[M].In:Newell Ed.Lectures in Appl Math,15,Providence:American Math Society,1974,143-196. [2] Newell A C.Solitons in Mathematics and Physics[M].Philadelphia:SIAM,1985. [3] Kruskal M D,Zabusky N J.Progress on the FPU nonlinear string problem[A].In:Kruskal M D Ed.Princeton Plasma Physics Laboratory Annual Rept[C].MATT-Q-21,Princeton:NJ,1963,61-83. [4] Ovler P J.Applications of Lie Group to Differential Equations[M].Berlin:Springer-Verlag,1989. [5] Blumann G W,Cole J D.Nonclassical symmetries of partial differential equations[J].J Math Mech,1969,10(5):1025-1032. [6] Clarkson P A,Kruskal M D.New similarity reductions of the Boussinesq equation[J].J Math Phys,1989,30(3):2201-2213. [7] Lou S Y.Nonclassical symmetry reductions for the dispersive wave equations in shallow water[J].J Math Phys,1992,33(10):4300-4305. [8] 闫振亚,张鸿庆.广义变系数KP方程的相似约化[J].应用数学和力学,2000,21(6):645-651. [9] Ablowitz M J,Ramani A,Segur H.A connection between nonlinear evolution equations and ordinary differential equations of P-type Ⅰ[J].J Math Phys,1980,21(4):715-725. [10] Ablowitz M J,Clarkson P A.Soliton Nonlinear Evolution Equations and Inverse Scatting[M].Cambridge:Cambridge University Press,1991. [11] Eilenberger G.Solitons-Mathematical Methods for Physics[M].New York:Springer-Verlag,1981.
计量
- 文章访问数: 2500
- HTML全文浏览量: 120
- PDF下载量: 724
- 被引次数: 0