Dispersionless Limit of Integrable Systems in 2 + 1 Dimensions

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


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):
$$\begin{array}{*{20}{c}} {{{x}_{y}} = A({{x}_{x}}),} \hfill \\ {{{x}_{t}} = B({{x}_{x}}).} \hfill \\ \end{array}$$


Compatibility Condition Unknown Coefficient Nonlinear Partial Differential Equation Dispersionless Limit Overdetermined Linear System 
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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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