Cooper-Shepard-Sodano重子的稳定性和动力学性质
Stability and dynamical properties of Cooper-Shepard-Sodano compactons
摘要：
推广了研究Rosenau-Hyman（RH）方程中双曲子的Pade近似方法，研究了Cooper-Shepard-Sodano（CSS）方程中单曲子及其相互作用的数值稳定性. CSS方程有一个保守的哈密顿量，它允许各种方法来研究分析的非线性稳定性的解决方案。我们研究了三种不同的牛顿解，发现它们是数值稳定的。类似于RH中微子之间的碰撞，CSS中微子在散射时以相同的连贯形状重新出现。散射后产生的小振幅波纹的时间演化取决于表征相应CSS方程的参数$l$和$p$的值。与RH散射的情况相比，CSS散射的模拟需要更小的人工粘性来获得数值稳定性。
英文摘要：
Extending a Pade approximant method used for studying compactons in the Rosenau-Hyman (RH) equation, we study the numerical stability of single compactons of the Cooper-Shepard-Sodano (CSS) equation and their pairwise interactions. The CSS equation has a conserved Hamiltonian which has allowed various approaches for studying analytically the nonlinear stability of the solutions. We study three different compacton solutions and find they are numerically stable. Similar to the collisions between RH compactons, the CSS compactons reemerge with same coherent shape when scattered. The time evolution of the small-amplitude ripple resulting after scattering depends on the values of the parameters $l$ and $p$ characterizing the corresponding CSS equation. The simulation of the CSS compacton scattering requires a much smaller artificial viscosity to obtain numerical stability, than in the case of RH compactons propagation.
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