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Wobbling kinks in ϕ4 and sine-Gordon theory

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Part of the Lecture Notes in Physics book series (LNP, volume 189)

Abstract

When the ϕ4 model admits a kink-solution, it also admits a wobbling king, which satisfies the boundary conditions of a kink, but possesses an internal degree of freedom. In this paper we develop a formal perturbation series for the wobbling kink in ϕ4 theory, and give the first two terms in the series explicitly. Then we prove that the formal series actually is asymptotic for a rahter long time [O (K ln(1/ε)), for a certain K]. Finally, we construct an exact 3-soliton solution of the sine-Gordon equation that also has the properties of a wobbling kink. For the sine-Gordon equation, the wobbling kink seems to be mildly unstable.

Keywords

Formal Series Secular Term Discrete Eigenvalue Kink Solution Inverse Scattering Transform 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    M. J. Rice, Phys. Lett. 71A, 152, (1979).Google Scholar
  2. [2]
    D. K. Campbell and A. R. Bishop, Nuclear Physics B 200, 297, (1982).Google Scholar
  3. [3]
    W. P. Su, J. R. Scriffer, and A. J. Heeger, Phys. Rev. Lett. 42, 1698, (1979).CrossRefGoogle Scholar
  4. [4]
    M. J. Rice and E. J. Mele, Solid State Comm. 35, 487, (1980)CrossRefGoogle Scholar
  5. [5]
    D. K. Campbell, J. F. Schonfeld, and C. A. Wingate, Resonance structure in kin-antikink interaction in ϕ 4 theory. (Preprint.)Google Scholar
  6. [6]
    M. J. Ablowitz, D. J. Kaup, A. C. Newell, and H. Segur, Phys. Rev. Lett. 30, 1262, (1973).CrossRefGoogle Scholar
  7. [7]
    M. J. Ablowitz, and H. Segur, Solitons and the Inverse Scattering Transform. SIAM, Philadelphia, 1981.Google Scholar
  8. [8]
    G. L. Lamb, Elements of Soliton Theory. Wiley-Interscience, New York, 1980.Google Scholar
  9. [9]
    I. M. Gel'fand and B. M. Levitan, American Mathematical Society Translation, Series 2, 1, 259, (1955).Google Scholar
  10. [10]
    G. G. Stokes, Trans. Cambridge Phil. Soc. 8, 81 (1847); (Papers 1, 197).Google Scholar
  11. [11]
    M. D. Kruskal, J. Math. Phys. 3, 806, (1962).CrossRefGoogle Scholar
  12. [12]
    D. W. McLaughlin, J. Math. Phys. 16, 96, (1975).CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1983

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