### Abstract

An averaging method for getting uniformly valid asymptotic approximations of the solution of hyperbolic systems of equations is presented. The averaged system of equations disintegrates into independent equations for non-resonance systems. We consider the resonance conditions for some classes of solutions. The averaged system can be solved numerically in the resonance case. The shallow water problem is considered as an example of the resonance system. Results of numerical experiments are presented.

Original language | English |
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Pages (from-to) | 458-470 |

Number of pages | 13 |

Journal | Journal of Nonlinear Mathematical Physics |

Volume | 8 |

Issue number | 4 |

Publication status | Published - 2001 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics

### Cite this

*Journal of Nonlinear Mathematical Physics*,

*8*(4), 458-470.

**Asymptotic Approximation of Hyperbolic Weakly Nonlinear Systems.** / Krylovas, A.; Čiegis, R.

Research output: Contribution to journal › Article

*Journal of Nonlinear Mathematical Physics*, vol. 8, no. 4, pp. 458-470.

}

TY - JOUR

T1 - Asymptotic Approximation of Hyperbolic Weakly Nonlinear Systems

AU - Krylovas, A.

AU - Čiegis, R.

PY - 2001

Y1 - 2001

N2 - An averaging method for getting uniformly valid asymptotic approximations of the solution of hyperbolic systems of equations is presented. The averaged system of equations disintegrates into independent equations for non-resonance systems. We consider the resonance conditions for some classes of solutions. The averaged system can be solved numerically in the resonance case. The shallow water problem is considered as an example of the resonance system. Results of numerical experiments are presented.

AB - An averaging method for getting uniformly valid asymptotic approximations of the solution of hyperbolic systems of equations is presented. The averaged system of equations disintegrates into independent equations for non-resonance systems. We consider the resonance conditions for some classes of solutions. The averaged system can be solved numerically in the resonance case. The shallow water problem is considered as an example of the resonance system. Results of numerical experiments are presented.

UR - http://www.scopus.com/inward/record.url?scp=0035643503&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035643503&partnerID=8YFLogxK

M3 - Article

VL - 8

SP - 458

EP - 470

JO - Journal of Nonlinear Mathematical Physics

JF - Journal of Nonlinear Mathematical Physics

SN - 1402-9251

IS - 4

ER -