Skip to main content

Second order Evolution Equations and Progressive Waves

  • Chapter
  • 571 Accesses

Part of the book series: Notes on Numerical Fluid Mechanics (NNFM) ((NNFM,volume 43))

Summary

Besides the classical first order evolution equations like Korteweg-de Vries, Burgers, a.o. equations, the second order evolution equations may be derived in order to model more complicated physical phenomena. Here the nerve pulse dynamics is modelled by a certain nonlinear second order equation. The physical motivation and the brief analysis are presented.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Whitham, G.B.: “Linear and nonlinear waves”, Wiley, New-York 1974.

    MATH  Google Scholar 

  2. Taniuti, T., Nishihara K.: “Nonlinear waves”, Pitman, Boston et al 1983.

    MATH  Google Scholar 

  3. Rudenko, O.V., Soluyan, S.I.: “Theoretical foundations of nonlinear acoustics”, Plenum, New York 1977.

    MATH  Google Scholar 

  4. Engelbrecht, J., Peipman, T., Valdek, U.: “Nonlinear effects in acoustics of solids”, in: M.F. Hamilton, D.T. Blackstock (eds), “Frontiers of nonlinear acoustics: Proceedings of 12th ISN A”, Elsevier, London 1990, pp. 535–540.

    Google Scholar 

  5. Engelbrecht, J.: “An introduction to asymmetric solitary waves”, Longman, Harlow 1991.

    MATH  Google Scholar 

  6. Scott, A.C., “Neurophysics”, Wiley, New York et el 1977.

    Google Scholar 

  7. Lieberstein, H.M.: “On the Hodgkin-Huxley partial differential equation”, Math. Bio-sci., 1 (1967) pp. 45–69.

    Article  Google Scholar 

  8. Engelbrecht, J.: “On theory of pulse transmission in a nerve fibre”, Proc. Royal Soc. London, A375 (1981) pp. 195–209.

    MathSciNet  Google Scholar 

  9. Reissig, R., Sansone, G., Conti R.: “Qualitative Theorie nichtlinearer Differentialgleichungen.” Edizioni Cremonese, Roma 1963.

    Google Scholar 

  10. Scott, A.C.: “Active and nonlinear wave propagation in electronics”, Wiley, New York et al 1970.

    Google Scholar 

  11. West, B.J.: “Fractal physiology and chaos in medicine”, World Scientific, Singapore et al 1990.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Andrea Donato Francesco Oliveri

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden

About this chapter

Cite this chapter

Engelbrecht, J. (1993). Second order Evolution Equations and Progressive Waves. In: Donato, A., Oliveri, F. (eds) Nonlinear Hyperbolic Problems: Theoretical, Applied, and Computational Aspects. Notes on Numerical Fluid Mechanics (NNFM), vol 43. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-87871-7_24

Download citation

  • DOI: https://doi.org/10.1007/978-3-322-87871-7_24

  • Publisher Name: Vieweg+Teubner Verlag

  • Print ISBN: 978-3-528-07643-6

  • Online ISBN: 978-3-322-87871-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics