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Solitary wave interactions in lattice systems with pure higher-order nonlinearity

机译:具有纯高阶非线性的晶格系统中的孤波相互作用

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In this paper, we investigate in detail the interactions of solitary waves in lattice systems with interaction potential V(q)=qnn, where n is 4,6,8..., through their all possible collision types, and establish a quantitative connection between the scattering property of solitary waves and the chaotic dynamics of the systems. Kink and antikink are excited in such lattice systems and the variation of their scattering effect with n is concerned. After a kink-antikink collision, the dominant interaction in the systems, if n is small, is that solitary waves pass through each other and the scattering effect increases with n; if n is large, solitary waves reflect back sometimes due to the influence of phase and this leads to a decrease of the scattering effect with n. The largest Lyapunov exponents of systems at fixed energy density first increase and then decrease with n, which is consistent with a variation of the scattering effect. The application of the special scattering behaviors between kink and antikink in information propagation is also discussed.
机译:在本文中,我们通过所有可能的碰撞类型,详细研究了具有相互作用势V(q)= qnn(其中n为4,6,8 ...)的晶格系统中孤立波的相互作用,并建立了定量连接孤波的散射特性与系统的混沌动力学之间的关系。扭结和抗扭结在这样的晶格系统中被激发,并关注其散射效应随n的变化。在扭结-抗扭结碰撞之后,系统中的主要相互作用(如果n小)是孤立波彼此穿过,并且散射效应随n增加;反之亦然。如果n大,则由于相位的影响,孤波有时会反射回来,这会导致n的散射效应降低。在固定能量密度下,系统的最大Lyapunov指数首先随n增大然后减小,这与散射效应的变化是一致的。还讨论了扭结和反扭结之间特殊的散射行为在信息传播中的应用。

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