### 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 language | English (US) |
---|---|

Pages (from-to) | 149-179 |

Number of pages | 31 |

Journal | Studies in Applied Mathematics |

Volume | 71 |

Issue number | 2 |

State | Published - Oct 1984 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Studies in Applied Mathematics*,

*71*(2), 149-179.

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

Research output: Contribution to journal › Article

*Studies in Applied Mathematics*, vol. 71, no. 2, pp. 149-179.

}

TY - JOUR

T1 - RESONANTLY INTERACTING WEAKLY NONLINEAR HYPERBOLIC WAVES. I. A SINGLE SPACE VARIABLE.

AU - Majda, Andrew

AU - Rosales, Rodolfo

PY - 1984/10

Y1 - 1984/10

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0021502758&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0021502758&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0021502758

VL - 71

SP - 149

EP - 179

JO - Studies in Applied Mathematics

JF - Studies in Applied Mathematics

SN - 0022-2526

IS - 2

ER -