Asymptotic investigation of a nonlinear model of string vibrations

Olga  Lavcel-Budko; Aleksandras  Krylovas; Paulius  Miškinis

doi:10.15388/LMR.B.2016.11

Articles

Olga Lavcel-Budko

Mykolo Romerio universitetas

Aleksandras Krylovas

Vilniaus Gedimino technikos universitetas

Paulius Miškinis

Vilniaus Gedimino technikos universitetas

Published 2016-12-20

https://doi.org/10.15388/LMR.B.2016.11

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Keywords

resonance
asymptotic methods
nonlinear waves
averaging

How to Cite

Lavcel-Budko O., Krylovas A. and Miškinis P. (2016) “Asymptotic investigation of a nonlinear model of string vibrations”, Lietuvos matematikos rinkinys, 57(B), pp. 60–64. doi: 10.15388/LMR.B.2016.11.

Abstract

The mathematical model of nonlinear oscillations of a weightless string is analysed. The uniformly valid asymptotic approximation in the long time interval, which is inversely proportional to the small parameter, is constructed. This asymptotic approximation is a solution of averaged along characteristics integro-differential system. A method for constructing special approximations of its solutions is proposed.

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