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2.034

Nonlinear Dynamics and Waves

3-0-9 units · Graduate

A unified treatment of nonlinear oscillations and wave phenomena with applications to mechanical, optical, geophysical, fluid, electrical and flow-structure interaction problems. Nonlinear free and forced vibrations; nonlinear resonances; self-excited oscillations; lock-in phenomena. Nonlinear dispersive and nondispersive waves; resonant wave interactions; propagation of wave pulses and nonlinear Schrodinger equation. Nonlinear long waves and breaking; theory of characteristics; the Korteweg-de Vries equation; solitons and solitary wave interactions. Stability of shear flows. Some topics and applications may vary from year to year.

Spring 2007

This graduate-level course provides a unified treatment of nonlinear oscillations and wave phenomena with applications to mechanical, optical, geophysical, fluid, electrical and flow-structure interaction problems.

Readings

  • The subject will be based on the material presented in the lectures. There is no required textbook. A general list of references is provided here.
    Listed reading
  • Minorsky, Nicholas. Nonlinear Oscillations . Melbourne, FL: Krieger Publishing, 1974. ISBN: 9780882751863.
    Listed reading
  • Nayfeh, Ali Hasan, and Dean T. Mook. Nonlinear Oscillations . New York, NY: John Wiley & Sons, 1995. ISBN: 9780471121428.
    Listed reading
  • Stoker, J. J. Nonlinear Vibrations in Mechanical and Electrical Systems . New York, NY: John Wiley & Sons, 1992. ISBN: 9780471570332.
    Listed reading
  • Den Hartog, J. P. Mechanical Vibrations . Mineola, NY: Dover Publications, 1985. ISBN: 9780486647852.
    Listed reading
  • Andronov, A. A., A. A. Vitt, and S. E. Khaikin. Theory of Oscillators . Mineola, NY: Dover Publications, 1987. ISBN: 9780486655086.
    Listed reading
  • Hayashi, Chihiro. Nonlinear Oscillations in Physical Systems . Princeton, NJ: Princeton University Press, 1986. ISBN: 9780691083834.
    Listed reading
  • Pippard, A. B. Response and Stability: An Introduction to the Physical Theory . Cambridge, UK: Cambridge University Press, 1985. ISBN: 9780521319942.
    Listed reading
  • Strogatz, Steven H. Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering . New York, NY: Perseus Books, 2001. ISBN: 9780738204536.
    Listed reading
  • Iooss, Gerard, and Daniel D. Joseph. Elementary Stability and Bifurcation Theory . New York, NY: Springer, 2004. ISBN: 9780387970684.
    Listed reading
  • Whitham, G. B. Linear and Nonlinear Waves . New York, NY: John Wiley & Sons, 2006. ISBN: 9780471359425.
    Listed reading
  • Craik, Alex D. D. Wave Interactions and Fluid Flows . Cambridge, UK: Cambridge University Press, 1999. ISBN: 9780521368292.
    Listed reading
  • Drazin, P. G. Nonlinear Systems . Cambridge, UK: Cambridge University Press, 1992. ISBN: 9780521404891.
    Listed reading
  • Newell, Alan C. Solitons in Mathematics and Physics . Philadelphia, PA: Society for Industrial and Applied Mathematics, 1987. ISBN: 9780898711967.
    Listed reading
  • Dauxois, Thierry, and Michel Peyrard. Physics of Solitons . Cambridge, UK: Cambridge University Press, 2006. ISBN: 9780521854214.
    Listed reading
  • The subject will be based on the material presented in the lectures. There is no required textbook. A general list of references will be provided (if you need additional references for a particular topic, please feel free to ask the instructor).
    Listed reading

Prerequisites & course information

Same subject as 1.685[J] , 18.377[J] Prereq: Permission of instructor G (Spring) 3-0-9 units

Sources