Multidimensional Nonlinear Equations

  • S. N. Gurbatov
  • O. V. Rudenko
  • A. I. Saichev
Part of the Nonlinear Physical Science book series (NPS)


Until now, we have analyzed the properties of one-dimensional fields as a function of time t and only one spatial coordinate. Such fields usually appear in an idealized, simplified description of real processes happening in the three-dimensional space. On the other hand, many ideas and methods of solving partial differential nonlinear equations for one-dimensional fields are in a natural way carried over to the richer with geometric and mechanical developments multidimensional case. Therefore, for completeness, let us discuss multidimensional equations related to those one-dimensional partial differential nonlinear equations of the first order which have been studied in the previous chapter. Complementary information on dynamics and statistics of three-dimensional fields of the hydrodynamic type can be found in [1–13].


Burger Equation Wilkinson Microwave Anisotropy Probe Integral Length Scale Initial Potential Nonlinear Stage 
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Copyright information

© Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • S. N. Gurbatov
    • 1
  • O. V. Rudenko
    • 2
  • A. I. Saichev
    • 3
  1. 1.Radiophysics DepartmentNizhny Novgorod State UniversityNizhny NovgorodRussia
  2. 2.Physics DepartmentMoscow State UniversityMoscowRussia
  3. 3.Radiophysics DepartmentNizhny Novgorod State UniversityNizhny NovgorodRussia

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