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Oscillations and Resonances
Hardcover
Series: de Gruyter Nonlinear Analysis and Applications, Book 23
General MathematicsGeneral Science
ISBN13: 9783110335545
Publisher: De Gruyter
Published: Apr 10 2017
Pages: 357
Weight: 1.65
Height: 0.90 Width: 6.80 Depth: 9.60
Language: English
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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