We discuss the effect of nonlinearity on the scattering dynamics of solitary waves. The pure nth power model with the interaction potential V （Х） = Х^n/n is present, which is a paradigm model in the study of solit...We discuss the effect of nonlinearity on the scattering dynamics of solitary waves. The pure nth power model with the interaction potential V （Х） = Х^n/n is present, which is a paradigm model in the study of solitary waves. The dependence of the scattering property on nonlinearity is closely related to the topological structures of the solitary waves. Moreover, for one of the four collision types, the rates of energy loss increase with the strength of nonlinearity and would reach 1 at n ≥ 10, which means that the two solitary waves would become of fragments completely after the collision.展开更多
We numerically study the interactions of solitary waves in granular media, by considering a chain of beads, which repel upon contact via the Hertz-type potential, V ∝ δ^n, with 5/2 ≤ n ≤ 3 and δ≥0, δ being the ...We numerically study the interactions of solitary waves in granular media, by considering a chain of beads, which repel upon contact via the Hertz-type potential, V ∝ δ^n, with 5/2 ≤ n ≤ 3 and δ≥0, δ being the bead-bead overlap. There are two collision types of solitary waves, overtaking collision and head-on collision, in the chain of beads. Our quantitative results show that after collision the large solitary wave gains energy and the small one loses energy for overtaking type while the large one loses energy, and the small one gains energy for head-on type. The scattering effects decrease with n for overtaking collision whereas increase with n for head-on collision.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos 10375039 and 90503008.
文摘We discuss the effect of nonlinearity on the scattering dynamics of solitary waves. The pure nth power model with the interaction potential V （Х） = Х^n/n is present, which is a paradigm model in the study of solitary waves. The dependence of the scattering property on nonlinearity is closely related to the topological structures of the solitary waves. Moreover, for one of the four collision types, the rates of energy loss increase with the strength of nonlinearity and would reach 1 at n ≥ 10, which means that the two solitary waves would become of fragments completely after the collision.
基金Supported by the National Natural Science Foundation of China under Grant Nos 10375039 and 90503008.
文摘We numerically study the interactions of solitary waves in granular media, by considering a chain of beads, which repel upon contact via the Hertz-type potential, V ∝ δ^n, with 5/2 ≤ n ≤ 3 and δ≥0, δ being the bead-bead overlap. There are two collision types of solitary waves, overtaking collision and head-on collision, in the chain of beads. Our quantitative results show that after collision the large solitary wave gains energy and the small one loses energy for overtaking type while the large one loses energy, and the small one gains energy for head-on type. The scattering effects decrease with n for overtaking collision whereas increase with n for head-on collision.
