eBook - ePub

Oscillations and Resonances

Name: Oscillations and Resonances
ISBN: 9783110382723

Sergey G. Glebov,

Oleg M. Kiselev,

Nikolai N. Tarkhanov,

357 pages
English
ePUB (mobile friendly)
Available on iOS & Android

eBook - ePub

Oscillations and Resonances

Sergey G. Glebov,

Oleg M. Kiselev,

Nikolai N. Tarkhanov,

About this book

This two-volume monograph presents new methods of construction of global asymptotics of solutions to nonlinear equations with small parameter. These allow one to match the asymptotics of various properties with each other in transition regions and to get unified formulas for the connection of characteristic parameters of approximate solutions.

This approach underlies modern asymptotic methods and gives a deep insight into crucial nonlinear phenomena in the natural sciences. These include the outset of chaos in dynamical systems, incipient solitary and shock waves, oscillatory processes in crystals, engineering applications, and quantum systems. Apart from being of independent interest, such approximate solutions serve as a foolproof basis for testing numerical algorithms.

This first volume presents asymptotic methods in oscillation and resonance problems described by ordinary differential equations, whereby the second volume will be devoted to applications of asymptotic methods in waves and boundary value problems.

Contents

Asymptotic expansions and series
Asymptotic methods for solving nonlinear equations
Nonlinear oscillator in potential well
Autoresonances in nonlinear systems
Asymptotics for loss of stability
Systems of coupled oscillators

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Yes, you can access Oscillations and Resonances by Sergey G. Glebov,Oleg M. Kiselev,Nikolai N. Tarkhanov in PDF and/or ePUB format, as well as other popular books in Mathematics & Differential Equations. We have over one million books available in our catalogue for you to explore.