Interactions between defects and propagating hydrodynamic solitons

doi:10.1088/1674-1056/19/8/080304

中国物理B ›› 2010, Vol. 19 ›› Issue (8): 80304-080304.doi: 10.1088/1674-1056/19/8/080304

Interactions between defects and propagating hydrodynamic solitons

潘军廷, 陈伟中, 郑鹭杰

The Key Laboratory of Modern Acoustics, Ministry of Education, and Institute of Acoustics, Nanjing University, Nanjing 210093, China

收稿日期:2009-11-12 修回日期:2009-12-10 出版日期:2010-08-15 发布日期:2010-08-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 10774072).

Interactions between defects and propagating hydrodynamic solitons

Pan Jun-Ting(潘军廷), Chen Wei-Zhong(陈伟中)^†, and Zheng Lu-Jie(郑鹭杰)

The Key Laboratory of Modern Acoustics, Ministry of Education, and Institute of Acoustics, Nanjing University, Nanjing 210093, China

Received:2009-11-12 Revised:2009-12-10 Online:2010-08-15 Published:2010-08-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 10774072).

摘要/Abstract

摘要： This paper studies the hydrodynamic solitons propagating along a long trough with a defective bed. The slight deviation from the plane in the bed serves as the depth defects. Based on the perturbation method, it finds that the free surface wave is governed by a Korteweg-de Vries (KdV) equation with a defect term (KdVD). The numerical calculations show that, for a single-convexity localized defect, the propagating soliton is decelerated as it comes into the defect region, and it is accelerated back to its initial velocity as it leaves, which has a dipole effect. As a result, its displacement is lagged in contrast to the uninfluenced one. And an up-step defect makes the propagating soliton decelerate simply. The opposite influence will occur for a single-concavity localized defect and a down-step one. The defect-induced influence on propagating hydrodynamic solitons depends on the polarity of defects, which agrees with that on non-propagating ones. However, the involved dipole effect of the single localized defect is not displayed in non-propagating cases.

Abstract: This paper studies the hydrodynamic solitons propagating along a long trough with a defective bed. The slight deviation from the plane in the bed serves as the depth defects. Based on the perturbation method, it finds that the free surface wave is governed by a Korteweg-de Vries (KdV) equation with a defect term (KdVD). The numerical calculations show that, for a single-convexity localized defect, the propagating soliton is decelerated as it comes into the defect region, and it is accelerated back to its initial velocity as it leaves, which has a dipole effect. As a result, its displacement is lagged in contrast to the uninfluenced one. And an up-step defect makes the propagating soliton decelerate simply. The opposite influence will occur for a single-concavity localized defect and a down-step one. The defect-induced influence on propagating hydrodynamic solitons depends on the polarity of defects, which agrees with that on non-propagating ones. However, the involved dipole effect of the single localized defect is not displayed in non-propagating cases.

Key words: propagating hydrodynamic soliton, defect, interaction

中图分类号: (Solitons)

05.45.Yv

02.60.-x (Numerical approximation and analysis)

潘军廷, 陈伟中, 郑鹭杰. Interactions between defects and propagating hydrodynamic solitons[J]. 中国物理B, 2010, 19(8): 80304-080304.

Pan Jun-Ting(潘军廷), Chen Wei-Zhong(陈伟中), and Zheng Lu-Jie(郑鹭杰). Interactions between defects and propagating hydrodynamic solitons[J]. Chin. Phys. B, 2010, 19(8): 80304-080304.

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Interactions between defects and propagating hydrodynamic solitons

Interactions between defects and propagating hydrodynamic solitons

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