Interactions between defects and propagating hydrodynamic solitons

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.