The usual (1+1)-dimensional Schwartz Boussinesq equation is extended to the (1+1)-dimensional space-time symmetric form and the general (n+1)-dimensional space-time symmetric form. These extensions are Painle...The usual (1+1)-dimensional Schwartz Boussinesq equation is extended to the (1+1)-dimensional space-time symmetric form and the general (n+1)-dimensional space-time symmetric form. These extensions are Painleve integrable in the sense that they possess the Painleve property. The single soliton solutions and the periodic travelling wave solutions for arbitrary dimensional space-time symmetric form are obtained by the Painleve-Backlund transformation.展开更多
Several global conclusions about an Ebenman's model of a population with competing juveniles and adults are derived in this paper. The problems about the number of non-trivial fixed points, the number of synchrono...Several global conclusions about an Ebenman's model of a population with competing juveniles and adults are derived in this paper. The problems about the number of non-trivial fixed points, the number of synchronous 2-cycles, and the number of attracting synchronous cycles are resolved. In a special case, the twice iteration of the 2-dimensional map can be reduced to a 1-dimensional map, and the existence of one or more continua of non-synchronous 2-cycles is pointed out. Numerical calculations are used to draw orbit diagrams which show complicated dynamics of this non-invertible 2-dimensional map. Experimental and field observational evidence is also discussed.展开更多
基金supported by the National Natural Science Foundation of China (Grant No 10575087)the Natural Science Foundation of Zhejiang Province,China (Grant No 102053)
文摘The usual (1+1)-dimensional Schwartz Boussinesq equation is extended to the (1+1)-dimensional space-time symmetric form and the general (n+1)-dimensional space-time symmetric form. These extensions are Painleve integrable in the sense that they possess the Painleve property. The single soliton solutions and the periodic travelling wave solutions for arbitrary dimensional space-time symmetric form are obtained by the Painleve-Backlund transformation.
文摘Several global conclusions about an Ebenman's model of a population with competing juveniles and adults are derived in this paper. The problems about the number of non-trivial fixed points, the number of synchronous 2-cycles, and the number of attracting synchronous cycles are resolved. In a special case, the twice iteration of the 2-dimensional map can be reduced to a 1-dimensional map, and the existence of one or more continua of non-synchronous 2-cycles is pointed out. Numerical calculations are used to draw orbit diagrams which show complicated dynamics of this non-invertible 2-dimensional map. Experimental and field observational evidence is also discussed.