Localized Waves in N + 1 Dimensions

  • A. Degasperis
Conference paper
Part of the Research Reports in Physics book series (RESREPORTS)


We give a method of costructing nonlinear Schroedinger equations in N+l dimensions, which are similar to the Davey-Stewartson equation as they are coupled to an additional scalar field, and possess, by construction, solutions describing interacting soliton-like objects.




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  1. [1]
    A. Degasperis and P. CSabatier, Phys. Lett. A (to be published).Google Scholar
  2. [2]
    P. C. Sabatier “Quest of multidimensional nonlinear equations with exponentially confined solutions”, in Inverse Problems 6, L29–L32 (1990).MathSciNetADSMATHCrossRefGoogle Scholar
  3. [3]
    P. CSabatier “Multidimensional nonlinear Schroedinger equations with exponentially confined solutions” to be published in Inverse Problems 6, 1990.Google Scholar
  4. [4]
    F. Calogero and S. De Lillo, Inverse Problems 3, 633–681 (1987), and F. Calogero in “What is integrability (for nonlinear PDEs)?”, V. E. Zakharov (ed.), Springer 1988.MathSciNetADSCrossRefGoogle Scholar
  5. [5]
    M. Boiti, J. J. P. Leon, L. Martina and F. Pempinelli, Phys. Lett. A 132, 432–439 (1988); A. S. Fokas and P. M. Santini, Phys. Rev. Lett. 63, 1329-1333 (1989).MathSciNetADSCrossRefGoogle Scholar
  6. [6]
    P. M. Santini, Physica D 41, 26–54 (1990); A. S. Fokas and P. M. Santini, Physica D (to be published); M. Boiti, J. J. P. Leon and F. Pempinelli “Bifurcations of Solitons in Multidimensions”, preprint Lecce University, 1990; J. Hietarinta and R. Hirota, Phys. Lett. A 145, 237 (1990).MathSciNetADSMATHCrossRefGoogle Scholar
  7. [7]
    A. S. Fokas and M. J. Ablowitz, J. Math. Phys. 25, 2494 (1984); M. Boiti, J. J. P. Leon, F. Pempinelli Phys. Lett. A 141, 96 (1989) and Phys. Lett. A 141, 101 (1989).MathSciNetADSMATHCrossRefGoogle Scholar
  8. [8]
    A. Degasperis, in “Inverse methods in action”, P. C Sabatier (ed.), Springer-Verlag, Berlin 1990.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • A. Degasperis
    • 1
    • 2
  1. 1.Dipartimento di FisicaUniversità “La Sapienza”RomaItaly
  2. 2.Instituto Nazionale di Fisica NucleareSezione di RomaItaly

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