RESONANTLY INTERACTING WEAKLY NONLINEAR HYPERBOLIC WAVES. I. A SINGLE SPACE VARIABLE.

Andrew Majda, Rodolfo Rosales

Research output: Contribution to journalArticle

Abstract

A systematic asymptotic theory for resonantly interacting weakly nonlinear hyperbolic waves in a single space variable is presented, treating the general situation when resonances occur in the hyperbolic system. Such resonances are the typical case when the hyperbolic system has a least three equations and when, for example, small-amplitude periodic initial data are prescribed. In the important physical example of the 3 multiplied by 3 system describing compressible fluid flow in a single space variable, the resonant asymptotic theory developed by the authors yields, as limit equations, a pair of inviscid Burgers equations coupled through a linear integral operator with known kernel defined through the initial data for the entropy wave.

Original languageEnglish (US)
Pages (from-to)149-179
Number of pages31
JournalStudies in Applied Mathematics
Volume71
Issue number2
StatePublished - Oct 1984

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Asymptotic Theory
Hyperbolic Systems
Compressible Fluid
Compressible Flow
Burgers Equation
Integral Operator
Linear Operator
Fluid Flow
Flow of fluids
Entropy
kernel

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

RESONANTLY INTERACTING WEAKLY NONLINEAR HYPERBOLIC WAVES. I. A SINGLE SPACE VARIABLE. / Majda, Andrew; Rosales, Rodolfo.

In: Studies in Applied Mathematics, Vol. 71, No. 2, 10.1984, p. 149-179.

Research output: Contribution to journalArticle

Majda, Andrew ; Rosales, Rodolfo. / RESONANTLY INTERACTING WEAKLY NONLINEAR HYPERBOLIC WAVES. I. A SINGLE SPACE VARIABLE. In: Studies in Applied Mathematics. 1984 ; Vol. 71, No. 2. pp. 149-179.
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