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Method of Stationary Phase and Short-wave Asymptotics

  • Yu. V. Egorov
  • M. A. Shubin
Part of the Encyclopaedia of Mathematical Sciences book series (volume 31)

Abstract

The method of stationary phase is one of the simplest methods for finding asymptotics of integrals, and yet it leads already to important results in the theory of hyperbolic equations and in various asymptotic problems for elliptic equations. With this method is closely associated the classical WKB method, so called in honour of the physicists Wentzel, Kramers and Brillouin who were the first to apply this method to the problems of quantum mechanics. The development of the WKB method leads to significant analytic and geometrical constructions, and one of the most important among these is the Maslov canonical operator which enables us to solve a large class of asymptotic problems.

Keywords

Cauchy Problem Asymptotic Solution Phase Function Hyperbolic Equation Modern Theory 
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

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Yu. V. Egorov
  • M. A. Shubin

There are no affiliations available

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