Acta Mechanica Sinica

, Volume 11, Issue 4, pp 289–306 | Cite as

Bidirectional soliton street

  • Theodore Yao-tsu Wu


The bidirectional long-wave model introduced by Wu (1994)[1] and Yih & Wu (1995)[2] is applied to evaluate interactions between multiple solitary waves progressing in both directions in a uniform channel of rectangular cross-section and undergoing collisions of two classes, one being head-on and the other overtaking collisions between these solitons. For a binary head-on collision, the two interacting solitary waves are shown to merge during a phase-locking period from which they reemerge separated, each asymptotically recovering its own initial identity while both being retarded in phase from their original pathlines. For a binary overtaking collision between a soliton of height α1 overtaking a weaker one of height α1, the two solition peaks are shown to either pass through each other or remain separated throughout the encounter according as α12 or <3, respectively. With no phase locking during the overtaking, the two solitary waves re-emerge afterwards with their initial forms recovered and with the stronger wave being advanced whereas the weaker one retarded in phase from their original pathlines. By extension, the theory is generalized to apply to uniform channels of arbitrary cross-sectional shape.

Key Words

bidirectional solition interaction solitary wave head-on collision overtaking collision 


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Copyright information

© Chinese Society of Theoretical and Applied Mechanics 1995

Authors and Affiliations

  • Theodore Yao-tsu Wu
    • 1
  1. 1.California Institute of TechnologyPasadenaUSA

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