Asymptotic Perturbation Methods

For Nonlinear Differential Equations in Physics

Attilio Maccari

• Publisher: Wiley-VCH
• Year: 2023
• Print ISBN: 9783527414215
• eBook ISBN: 9783527841738
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Mathematical Analysis

Asymptotic Perturbation Methods

Cohesive overview of powerful mathematical methods to solve differential equations in physics

Asymptotic Perturbation Methods for Nonlinear Differential Equations in Physics addresses nonlinearity in various fields of physics from the vantage point of its mathematical description in the form of nonlinear partial differential equations and presents a unified view on nonlinear systems in physics by providing a common framework to obtain approximate solutions to the respective nonlinear partial differential equations based on the asymptotic perturbation method.

Aside from its complete coverage of a complicated topic, a noteworthy feature of the book is the emphasis on applications. There are several examples included throughout the text, and, crucially, the scientific background is explained at an elementary level and closely integrated with the mathematical theory to enable seamless reader comprehension.

To fully understand the concepts within this book, the prerequisites are multivariable calculus and introductory physics.

Written by a highly qualified author with significant accomplishments in the field, Asymptotic Perturbation Methods for Nonlinear Differential Equations in Physics covers sample topics such as:

• Application of the various flavors of the asymptotic perturbation method, such as the Maccari method to the governing equations of nonlinear system
• Nonlinear oscillators, limit cycles, and their bifurcations, iterated nonlinear maps, continuous systems, and nonlinear partial differential equations (NPDEs)
• Nonlinear systems, such as the van der Pol oscillator, with advanced coverage of plasma physics, quantum mechanics, elementary particle physics, cosmology, and chaotic systems
• Infinite-period bifurcation in the nonlinear Schrodinger equation and fractal and chaotic solutions in NPDEs

Asymptotic Perturbation Methods for Nonlinear Differential Equations in Physics is ideal for an introductory course at the senior or first year graduate level. It is also a highly valuable reference for any professional scientist who does not possess deep knowledge about nonlinear physics.

Table of contents

• Cover
• Table of Contents
• Title Page
• Copyright
• About the Author
• Foreword
• Introduction
• 1 The Asymptotic Perturbation Method for Nonlinear Oscillators
• 2 The Asymptotic Perturbation Method for Remarkable Nonlinear Systems
• 3 The Asymptotic Perturbation Method for Vibration Control with Time-delay State Feedback
• 4 The Asymptotic Perturbation Method for Vibration Control by Nonlocal Dynamics
• 5 The Asymptotic Perturbation Method for Nonlinear Continuous Systems
• 6 The Asymptotic Perturbation Method for Dispersive Nonlinear Partial Differential Equations
• 7 The Asymptotic Perturbation Method for Physics Problems
• 8 The Asymptotic Perturbation Model for Elementary Particle Physics
• 9 The Asymptotic Perturbation Method for Rogue Waves
• 10 The Asymptotic Perturbation Method for Fractal and Chaotic Solutions
• 11 The Asymptotic Perturbation Method for Nonlinear Relativistic and Quantum Physics
• 12 Cosmology
• 13 Confinement and Asymptotic Freedom in a Purely Geometric Framework
• 14 The Asymptotic Perturbation Method for a Reverse Infinite-Period Bifurcation in the Nonlinear Schrodinger Equation
• Conclusion
• References
• Index
• End User License Agreement