Skip to main content
SpringerLink
Log in

Propagation of surface and internal solitary waves in nonuniform media

  • Published:
Applied Scientific Research Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Broussinesq J (1872) Théorie des ondes des remous qui se propagent le long d'un canal rectangulaire horizontal, en communiquant au liquide contenu dans ce canal des vitesses sensiblement pareilles de la surface au fond. J Math Pures Appl 17: 55–108

    Google Scholar 

  2. Broer LJF (1974) On the Hamiltonian Theory of Surface Waves. Appl Sci Res 29: 430–446

    Google Scholar 

  3. Broer LJF and Sluijter FW (1977) Stable Approximate Equations for Ion-acoustic Waves. Phys Fluids 20: 1458–1460

    Google Scholar 

  4. Djordjevic VD and Redekopp LG (1978) The Fission and Disintegration of Internal Solitary Waves Moving Over Two-Dimensional Topography. J Phys Ocean 8: 1016–1024

    Google Scholar 

  5. Grimshaw R (1970) The solitary wave in water of variable depth. J Fluid Mech 42: 639–656

    Google Scholar 

  6. Grimshaw R (1971) The solitary wave in water of variable depth, Part 2. J Fluid Mech 46: 611–622

    Google Scholar 

  7. Johnson RS (1973) Asymptotic solution of the Korteweg-deVries equation with slowly varying coefficients. J Fluid Mech 60: 813–824

    Google Scholar 

  8. Johnson RS (1973) On the Development of a Solitary Wave Moving Over an Uneven Bottom. Proc Camb Phil Soc 73: 183

    Google Scholar 

  9. Kakutani T (1971) Effects of an Uneven Bottom on Gravity Waves. J Phys Soc Japan 30: 272

    Google Scholar 

  10. Karpman VI and Maslov EM (1977) A Perturbation Theory for the Kortweg-deVries Equation. Phys Lett 60A: 307–308

    Google Scholar 

  11. Kaup DJ and Newell AC (1978) Solitons as Particles and Oscillators and in Slowly Varying Media: A Singular Perturbation Theory. Proc Roy Soc A361: 413–446

    Google Scholar 

  12. Knickerbocker CJ and Newell AC (1980) Shelves and the Korteweg-deVries equation. J Fluid Mech 98: 803–818

    Google Scholar 

  13. Knickerbocker CJ and Newell AC (1980) Internal Solitary Waves Near a Turning Point. Phys Lett, Vol 75A: 326–330

    Google Scholar 

  14. Knickerbocker CJ and Newell AC (1981) Reflections from Solitary Waves in Non-uniform Media, preprint

  15. Korteweg DJ and deVries G (1895) On the Change of Form of Long Waves advances in a Rectangular Canal, and on the New Type of Long Stationary Waves. Phil Mag 5, 39: 422

    Google Scholar 

  16. Leibovich S and Randall JD (1973) Amplification and Decay of Long Nonlinear Waves. J Fluid Mech 58: 481–493

    Google Scholar 

  17. Miles JW (1979) On the Korteweg-deVries equation for a gradually varying channel. J Fluid Mech 91: 181–190

    Google Scholar 

  18. Newell AC (1978) Soliton Perturbation and Nonlinear Focussing, Symposium on Nonlinear Structure and Dynamics in Condensed Matter. Solid State Physics Vol. 8, pp 52–68.

    Google Scholar 

  19. Peregrine DH (1967) Long Waves on a Beach. J Fluid Mech 27: 815

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical and Computer Science, Clarkson College, 13676, Potsdam, N.Y., USA

    Collen Knickerbocker & Alan C. Newell

Authors
  1. Collen Knickerbocker
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alan C. Newell
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Knickerbocker, C., Newell, A.C. Propagation of surface and internal solitary waves in nonuniform media. Applied Scientific Research 37, 111–126 (1981). https://doi.org/10.1007/BF00382622

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00382622

Keywords

Search

Navigation