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Dispersionless Limit of Integrable Systems in 2 + 1 Dimensions

  • V. E. Zakharov
Part of the NATO ASI Series book series (NSSB, volume 320)

Abstract

A general scheme for construction of dispersionless limits of 2 + 1 dimensional integrable systems was described first in the article [1]. Now we give its description in more details. Let us consider the following overdetermined system of two first—order nonlinear partial differential equations on a function x = x(x, y, t):
$$\begin{array}{*{20}{c}} {{{x}_{y}} = A({{x}_{x}}),} \hfill \\ {{{x}_{t}} = B({{x}_{x}}).} \hfill \\ \end{array}$$
(1)

Keywords

Compatibility Condition Unknown Coefficient Nonlinear Partial Differential Equation Dispersionless Limit Overdetermined Linear System 
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.
    V.E. Zakharov,Integrable systems in multidimensional spaces,Lecture Notes in Physics, Springer-Verlag, Berlin 153 (1982),190–216.Google Scholar
  2. 2.
    V.E.Zakharov,Benney equation and quasiclassical approximation in the inverse transform model, Funct. Anal. Appl. 14 (1980),15–24.zbMATHCrossRefGoogle Scholar
  3. 3.
    V.E.Zakharov,Multidimensional integrable systems, Proceedings of the International Congress of Mathematicians, August 1983, Warsaw 2 (1983),1225–1244.Google Scholar
  4. 4.
    A.V. Mikhailov, JETP Letters 30 (1979), 414–420.ADSGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • V. E. Zakharov
    • 1
    • 2
  1. 1.University of Arizona TucsonDepartment of MathematicsArizonaUSA
  2. 2.Landau Institute for Theoretical PhysicsMoscowRussia

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