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Nonlinear Oscillations and Waves in Dynamical Systems

  • Book
  • © 1996

Overview

Authors:
  1. P. S. Landa

    1. Department of Physics, Moscow State University, Moscow, Russia

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Part of the book series: Mathematics and Its Applications (MAIA, volume 360)

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Table of contents (27 chapters)

  1. Front Matter

    Pages i-xv
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  2. Introduction

    1. Introduction

      • P. S. Landa
      Pages 1-6

  4. Basic Dynamical Models of the Theory of Oscillations and Waves

    1. Front Matter

      Pages 33-33
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    2. Conservative systems

      • P. S. Landa
      Pages 35-57

    3. Non-conservative Hamiltonian systems and dissipative systems

      • P. S. Landa
      Pages 58-67

  5. Natural (Free) Oscillations and Waves in Linear and Non-Linear System

    1. Front Matter

      Pages 69-69
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    2. Natural oscillations of non-linear oscillators

      • P. S. Landa
      Pages 71-84

    3. Natural oscillations in systems of coupled oscillators

      • P. S. Landa
      Pages 85-105

    4. Natural waves in bounded and unbounded continuous media. Solitons

      • P. S. Landa
      Pages 106-136

  6. Forced Oscillations and Waves in Passive Systems

    1. Front Matter

      Pages 137-137
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    2. Oscillations of a non-linear oscillator excited by an external force

      • P. S. Landa
      Pages 139-155

    3. Oscillations of coupled non-linear oscillators excited by an external periodic force

      • P. S. Landa
      Pages 156-185

    4. Parametric oscillations

      • P. S. Landa
      Pages 186-201

    5. Waves in semibounded media excited by perturbations applied to their boundaries

      • P. S. Landa
      Pages 202-224

  7. Oscillations and Waves in Active Systems. Self-Oscillations and Auto-Waves

    1. Front Matter

      Pages 225-225
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Keywords

About this book

A rich variety of books devoted to dynamical chaos, solitons, self-organization has appeared in recent years. These problems were all considered independently of one another. Therefore many of readers of these books do not suspect that the problems discussed are divisions of a great generalizing science - the theory of oscillations and waves. This science is not some branch of physics or mechanics, it is a science in its own right. It is in some sense a meta-science. In this respect the theory of oscillations and waves is closest to mathematics. In this book we call the reader's attention to the present-day theory of non-linear oscillations and waves. Oscillatory and wave processes in the systems of diversified physical natures, both periodic and chaotic, are considered from a unified poin t of view . The relation between the theory of oscillations and waves, non-linear dynamics and synergetics is discussed. One of the purposes of this book is to convince reader of the necessity of a thorough study popular branches of of the theory of oscillat ions and waves, and to show that such science as non-linear dynamics, synergetics, soliton theory, and so on, are, in fact , constituent parts of this theory. The primary audiences for this book are researchers having to do with oscillatory and wave processes, and both students and post-graduate students interested in a deep study of the general laws and applications of the theory of oscillations and waves.

Authors and Affiliations

  • Department of Physics, Moscow State University, Moscow, Russia

    P. S. Landa

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