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    Kaplan, A.E. 1988. Bistable solitons of highly-nonlinear Schrödinger equations in nonlinear optics. Mathematical and Computer Modelling, Vol. 11, p. 106.

    Enns, R. H. Rangnekar, S. S. and Kaplan, A. E. 1987. ‘‘Robust’’ bistable solitons of the highly nonlinear Schrödinger equation. Physical Review A, Vol. 35, Issue. 1, p. 466.

    Enns, R. H. Rangnekar, S. S. and Kaplan, A. E. 1987. Bistable-soliton pulse propagation: Stability aspects. Physical Review A, Vol. 36, Issue. 3, p. 1270.

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    Rasmussen, J Juul and Rypdal, K 1986. Blow-up in Nonlinear Schroedinger Equations-I A General Review. Physica Scripta, Vol. 33, Issue. 6, p. 481.

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    Infeld, E. and Ziemkiewicz, J. 1981. Two-dimensional stability of large amplitude langmuir waves and solitons. Physics Letters A, Vol. 83, Issue. 7, p. 331.

    Laedke, E. W. and Spatschek, K. H. 1979. An energy principle for soliton solutions with higher nonlinearities. Journal of Plasma Physics, Vol. 22, Issue. 03, p. 477.


Transverse instability of soliton solutions to nonlinear Schrödinger equations

  • D. Anderson (a1), A. Bondeson (a1) and M. Lisak (a1)
  • DOI:
  • Published online: 01 March 2009

An inverstigation is made of the transverse instability of plane soliton solutions of the nonlinear Schrödinger equation, including the case of an exponential nonlinearity. The analysis is based on a variational method, where specific trial functions are applied for the perturbations. Explicit expressions for the growth rates are given, showing good agreement with numerical results.

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Yu. V. Kathshev & V. G. Makhankov 1976 Phys. Lett. 57A, 10.

P. Kaw , G. Schmidt & T. Wilcox 1973 Phys. Fluids, 16, 1522.

N. R. Pereira , R. N. Sudan & J. Denavit 1977 Phys. Fluids, 20, 271, 936.

G. Schmidt 1975 Phys. Rev. Lett. 34, 724.

K. H. Spatschek , P. K. Shukla & M. Y. Yu 1975 Phys. Lett. 54A, 419.

N. Yajima 1974 Progr. Theor. Phys. 52, 1066.

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Journal of Plasma Physics
  • ISSN: 0022-3778
  • EISSN: 1469-7807
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