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Spectral characterization of 2-D nonlinear coherent structures

  • J. Leon
  • M. Boiti
  • F. Pempinelli
Part III. Nonlinear Wave Propagation: Numerical and Theoretical Studies
Part of the Lecture Notes in Physics book series (LNP, volume 353)

Abstract

It is shown that a convenient choice of the definition of the spectral transform of the solutions of the Davey-Stewartson equation (or two-dimensional nonlinear Schrödinger equation) allows to characterize the 2-D nonlinear coherent structures by a point spectrum like in the one-dimensional case.

Keywords

Nonlinear Evolution Equation Point Spectrum Inverse Spectral Problem Spectral Transform Homogeneous Term 
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References

  1. [1]
    M. BOITI, J.JP. LEON, L. MARTINA, F. PEMPINELLI, “Scattering of localized solitons in the plane” Phys. Lett. A 132, 432 (1988)CrossRefGoogle Scholar
  2. [2]
    M. BOITI, J.JP. LEON, F. PEMPINELLI “A new spectral transform for the Davey Stewartson eq. I” Preprint PM 89/10, (Montpellier Feb. 1989) to appear in Phys. Lett. AGoogle Scholar
  3. [3]
    M. BOITI, J.JP. LEON, F. PEMPINELLI “A new spectral transform for the Kadomtsev-Petviashvili eq. I” Preprint PM 89/9 (Montpellier Feb 1989) to appear in Phys. Lett. A.Google Scholar
  4. [4]
    A.S. FOKAS, P.M. SANTINI “Solitons in multidimensions” Preprint INS # 106, Clarkson (Nov. 1988).Google Scholar
  5. [5]
    A.S. FOKAS, M.J. ABLOWITZ J. Math. Phys. 25, 2494 (1984)CrossRefGoogle Scholar
  6. [6]
    M. BOITI, J.JP. LEON, F. PEMPINELLI “Multidimensional solitons and their spectral transform”, Preprint PM 88/44 (Montpellier, October 1988). See also M. BOITI, J.JP. LEON, L. MARTINA, F. PEMPINELLI “Localized solitons in the plane” in “Nonlinear Evolution Equations: Integrability and Spectral Methods” Eds: A. DEGASPERIS, A.P. FORDY, M. IAKSHMANAN, Manchester Univ. Press (1989); and “Solitons in two dimensions” in “Integrable Systems and Applications” Eds M. BALABANE, P. LOCHAK, D.W. Mc IAUGHLIN, C. SULEM in Lecture Notes in Physics (1989).Google Scholar
  7. [7]
    A. DAVEY, K. STEWARTSON Proc. Roy. Soc. London A 338, 101 (1974)Google Scholar
  8. [8]
    F. CALOGERO, A. DEGASPERIS, Nuovo Limento B 32, 201 (1976)Google Scholar
  9. [9]
    S.V. MANAKOV, Physica D 3, 420 (1981)CrossRefGoogle Scholar
  10. [10]a
    J.JP. LEON: “On the nonlinear evolutions having nonanalytic dispersion relations” in “Some topics on inverse problems” Ed: P.C. SABATIER, World Scientific (Singapore 1988) andGoogle Scholar
  11. [10]b
    J.JP. LEON, F. PEMPINELLI: “Singular general evolutions in 1+1 and 2+1 dimensions” in “Nonlinear evolution equations: integrability and spectral methods” Eds.: A. DEGASPERIS, A.P. FORDY, M. LAKSHMANAN, Manchester University Press (1989).Google Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • J. Leon
    • 1
  • M. Boiti
    • 2
  • F. Pempinelli
    • 2
  1. 1.Laboratoire de Physique MathématiqueU.S.T.L.Montpellier Cedex 01France
  2. 2.Dipartimento di FisicaUniversitá di LecceLecceItalia

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