Nonlinear equations with small parameter. Volume 1, Oscillations and resonances / Sergey G. Glebov, Oleg M. Kiselev, Nikolai N. Tarkhanov.

Format:

Book

Author/Creator:

Glebov, Sergey G., author.

Kiselev, Oleg M., author.

Tarkhanov, Nikolai N., author.

Series:

De Gruyter series in nonlinear analysis and applications ; Volume 23/1.

De Gruyter Series in Nonlinear Analysis and Applications, 0941-813X ; Volume 23/1

Language:

English

Subjects (All):

Oscillations.

Physical Description:

1 online resource (340 pages).

Edition:

1st ed.

Place of Publication:

Berlin, [Germany] ; Boston, [Massachusetts] : De Gruyter, 2017.

Language Note:

In English.

Summary:

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

Contents:

Frontmatter

Preface

Contents

Introduction

1 Asymptotic expansions and series

2 Asymptotic methods for solving nonlinear equations

3 Perturbation of nonlinear oscillations

4 Nonlinear oscillator in potential well

5 Autoresonances in nonlinear systems

6 Asymptotics for loss of stability

7 Systems of coupled oscillators

Bibliography

Index

Notes:

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (ebrary, viewed May 4, 2017).

ISBN:

9783110382723

3110382725

9783110335682

3110335689

OCLC:

984625916