Remarks on the inverse scattering transform associated with toda equations

  • Mark J. Ablowitz
  • J. Villorroel
Conference paper
Part of the Lecture Notes in Physics book series


The Inverse Scattering Transforms used to solve both the 2+1 Toda equation and a novel reduction, the Toda differential-delay equations are outlined. There are a number of interesting features associated with these systems and the related scattering theory.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    R.S. Ward, Phil.Trans.Roy.Soc. London A415 (1985), 451ADSGoogle Scholar
  2. 2.
    L. Mason and G.A.J. Sparling, Phys.Lett. A137 (1989), 29ADSMathSciNetGoogle Scholar
  3. 3.
    S. Chakravarty and Mark J. Ablowitz, On reductions of the Self-Dual Yang-Mills Equations, in Painleve Transcendents, Ed. D. Levi and P. Winternitz, Plenum Press, 1992, p.331–343Google Scholar
  4. 4.
    Mark J. Ablowitz and H. Segur, Solitons and the inverse Scattering Transform, SIAM (1981) Phila., 425 pagesCrossRefzbMATHGoogle Scholar
  5. 5.
    Mark J. Ablowitz and P. Clarkson, Solitons, Nonlinear Evolution Equations and Inverse Scattering, Cambridge University Press 1991, 516 pagesGoogle Scholar
  6. 6.
    J. Villarroel and Mark J. Ablowitz, Physica D65 (1993) 48–70ADSMathSciNetGoogle Scholar
  7. 7.
    J. Villarroel and Mark J. Ablowitz, Phys. Lett. A (To be published)Google Scholar
  8. 8.
    J. Villarroel and Mark J. Ablowitz, J. Phys. A: Mathematics (To be published)Google Scholar
  9. 9.
    J. Villarroel, J. Phys. A: Mathematics 24 (1991), 3587CrossRefzbMATHADSMathSciNetGoogle Scholar
  10. 10.
    V. Lipovskii, S. Nikulichev. Proc. of Leningrad State Univ., 4 (1988), (in Russian)Google Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Mark J. Ablowitz
    • 1
  • J. Villorroel
    • 2
  1. 1.Program in Applied MathematicsUniversity of ColoradoBoulderUSA
  2. 2.Departamento de MatematicasUniversidad de SalamancaSalamancaSpain

Personalised recommendations