Other Standard Nonlinear Models of Higher Order

  • Alexander I. Saichev
  • Wojbor A. Woyczyński
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


This chapter builds on the material of Chap. 14 and reviews other standard nonlinear models that can be described by partial differential equations. We begin with the model equations of gas dynamics, expand the Burgers–KPZ model to the multidimensional case and the related concentration fields, study in detail the Korteweg–de Vries (KdV) equations, in which one can observe the creation of solitary waves (solitons), and finally, discuss nonlinear flows in porous media.


Burger Equation Initial Field Porous Medium Equation Passive Tracer Linear Parabolic Equation 
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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Alexander I. Saichev
    • 1
    • 2
  • Wojbor A. Woyczyński
    • 3
  1. 1.Department of Management, Technology, and EconomicsETH ZürichZürichSwitzerland
  2. 2.Department of Radio PhysicsUniversity of Nizhniy NovgorodNizhniy NovgorodRussia
  3. 3.Department of Mathematics, Applied Mathematics and Statistics, and Center for Stochastic and Chaotic Processes in Science and TechnologyCase Western Reserve UniversityClevelandUSA

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