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Solitary waves in stratified fluids and their interaction

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Abstract

A systematic procedure is proposed for obtaining solutions for solitary waves in stratified fluids. The stratification of the fluid is assumed to be exponential or linear. Its comparison with existing results for an exponentially stratified fluid shows agreement, and it is found that for the odd series of solutions the direction of displacement of the streamlines from their asymptotic levels is reversed when the stratification is changed from exponential to linear. Finally the interaction of solitary waves is considered, and the Korteweg-de Vries equation and the Boussinesq equation are derived. Thus the known solutions of these equations can be relied upon to provide the answers to the interaction problem.

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References

  1. Peters AS and Stoker JJ. Solitary waves in liquids having nonconstant density.Comm in Pure and Applied Math, 1960, XIII: 115–164

    MathSciNet  Google Scholar 

  2. Long RR. On the Boussinesq approximation and its role in the theory of internal waves.Tellus, 1965, 17: 46–52

    MathSciNet  Google Scholar 

  3. Benney DJ. Long nonlinear waves in fluid flows.J Math Physics, 1966, 45: 52–63

    MATH  MathSciNet  Google Scholar 

  4. Benjamin TB. Internal waves of finite amplitude and permanent form.J Fluid Mech, 1966, 25: 241–270

    Article  MATH  MathSciNet  Google Scholar 

  5. Gardner CS, Greene JM, Kruskal MD and Miura RM. Method for solving the Korteweg-de Vries equation.Phys Rev Lett, 1967, 19: 1095–1097

    Article  MATH  Google Scholar 

  6. Hirota R. Exact N-soliton solution of the wave equation of long waves in shallow water and in nonlinear lattices.J Math Phys, 1973, 14: 810–814

    Article  MATH  MathSciNet  Google Scholar 

  7. Yih CS. General solution for interaction of solitary waves including head-on collisions.Acta Mechanica Sinica (English Edition), 1993, 9(2): 97–101

    Article  MATH  Google Scholar 

  8. Dubreil-Jacotin ML. Complément à une note antérieure sur les ondes de type permanent dans les liquides hétérogènes.Atti Acad Lincei Rend Cl Sci Fis Mat Nat, 1935, 21(6): 344–346

    MATH  Google Scholar 

  9. Long RR. Some aspects of the flow of stratified fluids, I. A theoretical investigation.Tellus, 1953, 5: 422–457

    Google Scholar 

  10. Ablowitz MJ and Segur H. Solitons and the Inverse Scattering Transform.Soc Ind Appl Math, Philadelphia, 1981: 290–296

  11. Hirota R. Exact solution of the Korteweg-de Vries equation for multiple collisions of solitons.Phys Rev Lett, 1971, 27: 1192–1194

    Article  MATH  Google Scholar 

  12. Miles JW. On internal solitary waves.Tellus, 1979, 31: 456–462

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. The University of Michigan, 48109, Ann Arbor, Michigan, USA

    Chia-Shun Yih

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  1. Chia-Shun Yih
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Yih, CS. Solitary waves in stratified fluids and their interaction. Acta Mech Sinica 9, 193–209 (1993). https://doi.org/10.1007/BF02486797

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  • DOI: https://doi.org/10.1007/BF02486797

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