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A variational principle for nonlinear water waves

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This paper is concerned with a variational formulation of non-axisymmetric water waves and of two-dimensional surface waves in a running stream of finite depth. The full set of equations of motions for the non-axisymmetric water wave problem in cylindrical polar coordinates and for the two-dimensional surface waves in the running stream in Cartesian coordinates is obtained from a Lagrangian function which is equal to the pressure.

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References

  1. Stoker, J. J.: Water waves. Interscience 1957.

  2. Debnath, L., Rosenblat, S.: The ultimate approach to the steady state in the generation of waves on a running stream. Quart. J. Math. and Appl. Math.22, 221–233 (1969).

    Google Scholar 

  3. Puri, K. K.: Waves on a shear flow. Bull. Austral. Math. Soc.11, 263–277 (1974).

    Google Scholar 

  4. Wehausen, J. V., Laitone, E. V.: Surface waves, in: Flügge, S., ed.: Handbuch der Physik, Vol. IX, Berlin: Springer-Verlag 1960.

    Google Scholar 

  5. Debnath, L.: On initial development of axisymmetric waves in fluids of finite depth. Proc. Nat. Inst. Sci. India35, 567–585 (1969).

    Google Scholar 

  6. Mondal, C. R.: Uniform asymptotic analysis of shallow-water waves due to a periodic surface pressure. Quart. Appl. Math. XLIV, 133–140 (1986).

    Google Scholar 

  7. Mahanti, N. C.: Small-amplitude internal waves due to an oscillatory pressure. Quart. Appl. Math.37, 92–97 (1979).

    Google Scholar 

  8. Debnath, L.: On transient development of surface waves. Zeits. für Angewandte Mathematik und Physik19, 948–961 (1968).

    Google Scholar 

  9. Mikhlin, S.: Variational methods in mathematical physics, Oxford: Pergamon 1964.

    Google Scholar 

  10. Arthurs, A. M.: Complementary variational principles. Oxford University Press 1970.

  11. Gelfand, I. M., Fomin, S. V.: Calculus of variations (Translated by Silverman, R. A.), Englewood Cliffs, N. J.: Prentice-Hall 1963.

    Google Scholar 

  12. Myint-U, T., Debnath, L.: Partial differential equations for Scientists and Engineers, third ed., Amsterdam North Holland 1987.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Central Florida, 32816, Orlando, FL, USA

    L. Debnath

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  1. L. Debnath
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Debnath, L. A variational principle for nonlinear water waves. Acta Mechanica 72, 155–160 (1988). https://doi.org/10.1007/BF01176549

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  • DOI: https://doi.org/10.1007/BF01176549

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