Compactons: Solitons with finite wavelength.
Compactons: Solitons with finite wavelength.
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DOI：
10.1103/physrevlett.70.564
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发表时间：
1993-02
影响因子：
8.6
通讯作者：
P. Rosenau;P. Rosenau;J. Hyman;J. Hyman
中科院分区：
文献类型：
--
作者：
P. Rosenau;P. Rosenau;J. Hyman;J. Hyman
The understand the role of nonlinear dispersion in pattern formation, we introduce and study Korteweg\char21{}de Vries\char21{}like equations wtih nonlinear dispersion: ${\mathit{u}}_{\mathit{t}}$+(${\mathit{u}}^{\mathit{m}}$${)}_{\mathit{x}}$+(${\mathit{u}}^{\mathit{n}}$${)}_{\mathit{x}\mathit{x}\mathit{x}}$=0, m,ng1. The solitary wave solutions of these equations have remarkable properties: They collide elastically, but unlike the Korteweg\char21{}de Vries (m=2, n=1) solitons, they have compact support. When two ``compactons'' collide, the interaction site is marked by the birth of low-amplitude compacton-anticompacton pairs. These equations seem to have only a finite number of local conservation laws. Nevertheless, the behavior and the stability of these compactons is very similar to that observed in completely integrable systems.
The understand the role of nonlinear dispersion in pattern formation, we introduce and study Korteweg\char21{}de Vries\char21{}like equations wtih nonlinear dispersion: ${\mathit{u}}_{\mathit{t}}$+(${\mathit{u}}^{\mathit{m}}$${)}_{\mathit{x}}$+(${\mathit{u}}^{\mathit{n}}$${)}_{\mathit{x}\mathit{x}\mathit{x}}$=0, m,ng1. The solitary wave solutions of these equations have remarkable properties: They collide elastically, but unlike the Korteweg\char21{}de Vries (m=2, n=1) solitons, they have compact support. When two ``compactons'' collide, the interaction site is marked by the birth of low-amplitude compacton-anticompacton pairs. These equations seem to have only a finite number of local conservation laws. Nevertheless, the behavior and the stability of these compactons is very similar to that observed in completely integrable systems.