Journal of Mathematical Physics
Feedback | Help | Exit
   
 
 
 
Previous Article
Hyperspherical harmonics with arbitrary arguments
The derivation scheme for hyperspherical harmonics (HSH) with arbitrary arguments is proposed. It is demonstrated that HSH can be presented as the product of HSH corresponding to spaces with lower dim...
Next Article
Integration of Grassmann variables over invariant functions on flat superspaces
We study integration over functions on superspaces. These functions are invariant under a transformation which maps the whole superspace onto the part of the superspace which only comprises purely com...

Canonical Hamiltonians for waves in inhomogeneous media

J. Math. Phys. 50, 013527 (2009); doi:10.1063/1.3054275

Published 15 January 2009

You are not logged in to this journal. Log in

Boris Gershgorin,1 Yuri V. Lvov,2 and Sergey Nazarenko3
1Courant Institute, New York University, New York, New York 10012, USA
2Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, New York 12180, USA
3Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom
We obtain a canonical form of a quadratic Hamiltonian for linear waves in a weakly inhomogeneous medium. This is achieved by using the Wentzel–Kramers–Brillouin representation of wave packets. The canonical form of the Hamiltonian is obtained via the series of canonical Bogolyubov-type and near-identical transformations. Various examples of the application illustrating the main features of our approach are presented. The knowledge of the Hamiltonian structure for linear wave systems provides a basis for developing a theory of weakly nonlinear random waves in inhomogeneous media generalizing the theory of homogeneous wave turbulence. ©2009 American Institute of Physics
History: Received 7 July 2008; accepted 24 November 2008; published 15 January 2009
Permalink: http://link.aip.org/link/?JMAPAQ/50/013527/1
BUY THIS ARTICLE   (US$28)
Download PDF (315 kB) View Cart

KEYWORDS and PACS

Keywords
PACS
  • 05.40.-a
    Fluctuation phenomena, random processes, noise, and Brownian motion
  • 02.50.-r
    Probability theory, stochastic processes, and statistics
  • 02.30.-f
    Function theory, analysis
  • YEAR: 2009

RELATED DATABASES


To view database links for this article,
you need to log in.
To view database links for this article,
you need to log in.

PUBLICATION DATA

ISSN:
0022-2488 (print)   1089-7658 (online)
Publisher:
AIP is a member of CrossRef AIP

REFERENCES (29)
View in Separate Window/Tab
For access to fully linked references, you need to log in. For access to fully linked references, you need to Log in.
  1. V. I. Arnold, Mathematical Methods of Classical Mechanics (Springer-Verlag, Berlin, 1978).
  2. A. Pushkarev, D. Resio, and V. Zakharov, Physica D 184, 29 (2003).
  3. A. S. Monin and L. I. Piterbarg, Dokl. Akad. Nauk SSSR 295, 816 (1987).
  4. A. M. Balk, V. E. Zakharov, and S. V. Nazarenko, Sov. Phys. JETP 71, 249 (1990).
  5. Yu. Lvov, E. Tabak, Phys. Rev. Lett. 87, 168501 (2001).
  6. S. Galtier, S. V. Nazarenko, A. C. Newell, and A. Pouquet, J. Plasma Phys. 63, 447 (2000).
  7. V. E. Zakharov and S. V. Nazarenko, Physica D 201, 203 (2005).
  8. Y. V. Lvov, S. Nazarenko, and R. West, Physica D 184, 333 (2003).
  9. A. A. Galeev and R. Z. Sagdeev, in Reviews of Plasma Physics, edited by M. A. Leontovich (Consultants Bureau, New York, 1973), Vol. 6.
  10. V. E. Zakharov, V. S. Lvov, and G. Falkovich, Kolmogorov Spectra of Turbulence (Springer-Verlag, Berlin, 1992).
  11. A. N. Pushkarev and V. E. Zakharov, Physica D 135, 98 (2000).
  12. V. E. Zakharov, Proceedings of IUTAM Meeting on Wave Breaking, Sydney, 1991, edited by M. L. Banner and R. H. Y. Grimshaw (Springer-Verlag, Berlin, 1992), pp. 69–91.
  13. G. Wentzel, Z. Phys. 38, 518 (1926).
  14. H. A. Kramers, Z. Phys. 39, 828 (1926).
  15. L. Brillouin, Compt. Rend. 183, 24 (1926).
  16. P. Janssen, The Interaction of Ocean Waves and Wind (Cambridge University Press, Cambridge, 2004).
  17. L. D. Landau and E. M. Lifshitz, Statistical Physics, Course of Theoretical Physics Vol 5 (Pergamon, New York, 1969).
  18. E. M. Lifshitz and L. P. Pitaevskii, Physical Kinetics, Course of Theoretical Physics Vol 10 (Butterworth-Heinemann, Washington, DC, 1981).
  19. S. Mallat, A Wavelet Tour of Signal Processing (Academic, New York, 1998).
  20. V. S. Lvov and A. M. Rubenchik, Sov. Phys. JETP 45, 67 (1977)
    21. also at V. S. Lvov, Fundamental of Nonlinear Physics, Lecture Notes, Eq. (7.8), www.lvov.weizmann.ac.il.
  21. S. N. Bose, Z. Phys. 26, 178 (1924).
  22. A. Einstein, Sitzungsber. Preuss. Akad. Wiss., Phys. Math. Kl. 22, 261 (1924)
    23. Reprinted in The collected papers of Albert Einstein, edited by J. Stachel, Princeton University Press, Princeton, 1989).
  23. Albert Einstein, Sitzungsber. Preuss. Akad. Wiss., Phys. Math. Kl. 23, 3 (1925)
    24. reprinted in The Collected Papers of Albert Einstein, edited by J. Stachel (Princeton University Press, Princeton, 1989).
  24. M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, Science 269, 198 (1995).
  25. C. C. Bradley, C. A. Scakett, J. J. Tollett, and R. G. Hulet, Phys. Rev. Lett. 75, 1687 (1995).
  26. K. B. Davis, M. -O. Mewes, M. R. Andrews, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, Phys. Rev. Lett. 75, 3969 (1995).
  27. L. P. Pitaevskii, Zh. Eksp. Teor. Fiz. 40, 646 (1961)
    28. [Sov. Phys. JETP 13, 451 (1961)].
  28. A. A. Vedenov, A. V. Gordeev, and L. I. Rudakov, Plasma Phys. 9, 719 (1967).
  29. A. I. Dyachenko, S. V. Nazarenko, and V. E. Zakharov, Phys. Lett. A 165, 330 (1992).

CITING ARTICLES
For access to citing articles, you need to log in.
For access to citing articles, you need to Log in.


Copyright © American Institute of Physics