Dispersive shock wave interactions and asymptotics.
Dispersive shock wave interactions and asymptotics.
复制标题
色散冲击波相互作用和渐进。
DOI：
10.1103/physreve.87.022906
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
D. Baldwin
中科院分区：
文献类型：
--
作者：
M. Ablowitz;D. Baldwin
色散激波（DSWs）是发生在弱色散和弱非线性系统中的重要物理现象。Korteweg-de Vries （KdV）方程是具有弱色散和弱二次非线性的系统的通用模型。这里我们证明了对于一般的步进数据，KdV方程的长时间渐近解是一个单相DSW；该DSW是基于边界数据的“最大”可能DSW。我们利用逆散射变换和匹配渐近展开式找到了这个渐近解。因此，虽然多步数据在中间阶段演变为多相动态，但这些相互作用的DSW最终会在大时间内合并形成单相DSW。
Dispersive shock waves (DSWs) are physically important phenomena that occur in systems dominated by weak dispersion and weak nonlinearity. The Korteweg-de Vries (KdV) equation is the universal model for systems with weak dispersion and weak, quadratic nonlinearity. Here we show that the long-time-asymptotic solution of the KdV equation for general, steplike data is a single-phase DSW; this DSW is the "largest" possible DSW based on the boundary data. We find this asymptotic solution using the inverse scattering transform and matched-asymptotic expansions. So while multistep data evolve to have multiphase dynamics at intermediate times, these interacting DSWs eventually merge to form a single-phase DSW at large time.