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Multidimensional Nonlinear Equations

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

Abstract

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].

Keywords

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