Solitary Waves in Layered Nonlinear Media
Solitary Waves in Layered Nonlinear Media
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DOI：
10.1137/s0036139902408151
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发表时间：
2003
期刊：
影响因子：
--
通讯作者：
Darryl H. Yong;R. LeVeque
中科院分区：
文献类型：
--
作者：
Darryl H. Yong;R. LeVeque
我们研究一维周期性层状介质中的纵向弹性应变波，在具有不同密度和应力应变关系的两种材料之间交替。如果阻抗不同，则会由于界面处的反射而出现色散效应。当应力-应变关系是非线性时，色散和非线性的结合导致出现像孤子一样相互作用的孤立波。我们研究这些孤立波的标度特性，并推导出包含色散项的均质方程组。我们证明，这些方程的伪谱解与使用高分辨率有限体积法的层状介质中双曲守恒定律的直接解非常一致。对于特定参数，我们还展示了分层介质如何与具有离散孤子解的 Toda 晶格相关。
We study longitudinal elastic strain waves in a one-dimensional periodically layered medium, alternating between two materials with different densities and stress-strain relations. If the impedances are different, dispersive effects are seen due to reflection at the interfaces. When the stress-strain relations are nonlinear, the combination of dispersion and nonlinearity leads to the appearance of solitary waves that interact like solitons. We study the scaling properties of these solitary waves and derive a homogenized system of equations that includes dispersive terms. We show that pseudospectral solutions to these equations agree well with direct solutions of the hyperbolic conservation laws in the layered medium using a high-resolution finite volume method. For particular parameters we also show how the layered medium can be related to the Toda lattice, which has discrete soliton solutions.