Nonlinear physics, from vibration control to rogue waves and beyond / Attilio Maccari.

Format:

Book

Author/Creator:

Maccari, Attilio, author.

Language:

English

Subjects (All):

Nonlinear theories.

Perturbation (Mathematics).

Physical Description:

1 online resource (x, 298 pages) : illustrations

Other Title:

Nonlinear physics from vibration control to rogue waves and beyond

Place of Publication:

Newcastle upon Tyne, England : Cambridge Scholars Publishing, 2022.

Summary:

"This textbook is devoted to nonlinear physics, using the asymptotic perturbation method as a mathematical tool. The theory is developed systematically, starting with nonlinear oscillators, limit cycles and their bifurcations, followed by iterated nonlinear maps, continuous systems, nonlinear partial differential equations (NPDEs) and culminating with infinite-period bifurcation in the nonlinear Schrodinger equation and fractal and chaotic solutions in NPDEs.A remarkable feature of the book is its emphasis on applications. It offers several examples, and the scientific background is explained at an elementary level and closely integrated with the mathematical theory. In addition, it is ideal for an introductory course at the senior or first-year graduate level."--Provided by publisher.

Contents:

Introduction

Part I: The Asymptotic Perturbation Method

Nonlinear Oscillators

Bifurcations and Nonlinear Oscillators

Vibration Control with Time Delay State Feedback

Vibration Control with a Non-Local Feedback

Part II: The AP Method for Nonlinear Partial Differential Equations (NPDEs)

How to Find Integrable Nonlinear Equations

The AP Method Applied to a Weak Lax Pair Formulation for a New Integrable Nonlinear Equation in 2+1 Dimensions

Part III: The AP Method Applied in Physical Problems

Nonlinear Water Waves

Interacting Dromions for Electron Acoustic Waves

Chaos, Solitons and Fractals in the Nonlinear Dirac Equation

Splitting Frequencies for Resonant Solutions in Central Fields

Approximate Particle-like Solutions for a Nonlinear Relativistic Scalar Complex Field Model in 3+1 Dimensions

An Integrable Nonlinear System from the Kadomtsev-Petviashvili Equation

The Primary Resonance for the Nonlinear Schrodinger Equation in 2+1 Dimensions

A Perturbative Approach to the Born-Infeld Equation

Conclusion.

Notes:

Includes bibliographical references (pages 287-298).

Description based on online resource (viewed Dec 4, 2023), publisher-supplied metadata and other sources.

Other Format:

Print version: Maccari, Attilio Nonlinear Physics, from Vibration Control to Rogue Waves and Beyond

ISBN:

9781527588189

1527588181

OCLC:

1371141968