Journal of Soviet Mathematics

, Volume 31, Issue 6, pp 3307–3316 | Cite as

Multidimensional nonlinear integrable systems and methods for constructing their solutions

  • V. E. Zakharov
  • S. V. Manakov


A new method for constructing multidimensional nonlinear integrable systems and their solutions by means of a nonlocal Riemann problem is presented. This is the natural generalization of the method of the local Riemann problem to the case of several space variables and includes the well-known Zakharov-Shabat method of dressing by Volterra operators.


Integrable System Space Variable Natural Generalization Riemann Problem Volterra Operator 
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Copyright information

© Plenum Publishing Corporation 1985

Authors and Affiliations

  • V. E. Zakharov
  • S. V. Manakov

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