JMP Nameplate
  • Volume/Page
  • Keyword
  • DOI
  • Citation
  • Advanced
   
 
 
 

Flickr Twitter UniPHY Group iResearch App Facebook

Journal of Mathematical Physics / Volume 23 / Issue 6

J. Math. Phys. 23, 988 (1982); http://dx.doi.org/10.1063/1.525467 (15 pages)

New Stokes’ line in WKB theory

H. L. Berk1, William McCay Nevins2, and K. V. Roberts3

1Institute for Fusion Studies, University of Texas, Austin, Texas 78712
2Lawrence Livermore National Laboratory, Livermore, California 94550
3Euratom/UKAEA Fusion Association, Culham Laboratory, Abingdon, Oxon OX 14 3DB, United Kingdom

The WKB theory for differential equations of arbitrary order or integral equations in one dimension is investigated. The rules previously stated for the construction of Stokes’ lines for Nth‐order differential equations, N⩾3, or integral equations are found to be incomplete because these rules lead to asymptotic forms of the solutions that depend on path. This paradox is resolved by the demonstration that new Stokes’ lines can arise when previously defined Stokes’ lines cross. A new formulation of the WKB problem is given to justify the new Stokes’ lines. With the new Stokes’ lines, the asymptotic forms can be shown to be independent of path. In addition, the WKB eigenvalue problem is formulated, and the global dispersion relation is shown to be a functional of loop integrals of the action.

KEYWORDS and PACS

Keywords

DIFFERENTIAL EQUATIONS, INTEGRAL EQUATIONS, ONE−DIMENSIONAL CALCULATIONS, WKB APPROXIMATION, ASYMPTOTIC SOLUTIONS, EIGENVALUES, DISPERSION RELATIONS

PACS

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.525467

PUBLICATION DATA

ISSN

0022-2488 (print)  
1089-7658 (online)

For access to fully linked references, you need to log in.
    W. H. Furry, Phys. Rev. 71, 360 (1947).

    H. L. Berk and D. L. Book, Phys. Fluids 12, 649 (1969PFLDAS000012000003000649000001).

    H. L. Berk and D. Pfirsch, J. Math. Phys. 21, 2054 (1980JMAPAQ000021000008002054000001).

    H. L. Berk, M. N. Rosenbluth, and R. N. Sudan, Phys. Fluids 9, 1606 (1966PFLDAS000009000008001606000001).

    T. H. Stix, Phys. Rev. Lett. 15, 878 (1965).

    D. Gorman, Phys. Fluids 9, 1262 (1966PFLDAS000009000006001262000001).

    R. E. Aamodt and D. L. Book, Phys. Fluids 9, 143 (1966PFLDAS000009000001000143000001).

    L. D. Pearlstein and D. Bhadra, Phys. Fluids 12, 213 (1969PFLDAS000012000001000213000001).

    H. Sanuki, T. Watanabe, and M. Watanabe, Phys. Fluids 23, 158 (1980PFLDAS000023000001000158000001).

    D. Watson, Phys. Fluids 23, 2485 (1981PFLDAS000023000012002485000001).

    H. L. Berk, L. D. Pearlstein, J. D. Callen, C. W. Horton, and M. N. Rosenbluth, Phys. Rev. Lett. 22, 876 (1969).


For access to citing articles, you need to log in.



Close

Google Calendar

ADVERTISEMENT

Your Recent History Recent History Help

Recently Viewed

  1. New Stokes’ line in WKB theory
  2. Erratum: Adjoints of nondensely defined Hilbert space operators [J. Math. Phys. 22, 1619 (1981)]
  3. Erratum: Nonuniqueness in the inverse source problem in acoustics and electromagnetics [J. Math. Phys. 18, 194 (1977)]
  4. Erratum: Structure and representations of the symmetry group of the four‐dimensional cube [J. Math. Phys. 23, 944 (1982)]
  5. A new mathematical formulation of accelerated observers in general relativity. I
Go to AIP Home
Copyright © American Institute of Physics
close