Nonlinear Dynamics [E-Book] : Integrability, Chaos and Patterns / by M. Lakshmanan, S. Rajasekar.
Integrability, chaos and patterns are three of the most important concepts in nonlinear dynamics. These are covered in this book from fundamentals to recent developments. The book presents a self-contained treatment of the subject to suit the needs of students, teachers and researchers in physics, m...
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Full text |
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Personal Name(s): | Lakshmanan, M., author |
Rajasekar, S., author | |
Imprint: |
Berlin, Heidelberg :
Springer,
2003
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Physical Description: |
XX, 620 p. online resource. |
Note: |
englisch |
ISBN: |
9783642556883 |
DOI: |
10.1007/978-3-642-55688-3 |
Series Title: |
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Advanced Texts in Physics
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Subject (LOC): |
- 1. What is Nonlinearity?
- 2. Linear and Nonlinear Oscillators
- 3. Qualitative Features
- 4. Bifurcations and Onset of Chaos in Dissipative Systems
- 5. Chaos in Dissipative Nonlinear Oscillators and Criteria for Chaos
- 6. Chaos in Nonlinear Electronic Circuits
- 7. Chaos in Conservative Systems
- 8. Characterization of Regular and Chaotic Motions
- 9. Further Developments in Chaotic Dynamics
- 10. Finite Dimensional Integrable Nonlinear Dynamical Systems
- 11. Linear and Nonlinear Dispersive Waves
- 12. Korteweg—de Vries Equation and Solitons
- 13. Basic Soliton Theory of KdV Equation
- 14. Other Ubiquitous Soliton Equations
- 15. Spatio-Temporal Patterns
- 16. Nonlinear Dynamics: From Theory to Technology
- A. Elliptic Functions and Solutions of Certain Nonlinear Equations
- Problems
- B. Perturbation and Related Approximation Methods
- B.1 Approximation Methods for Nonlinear Differential Equations
- B.2 Canonical Perturbation Theory for Conservative Systems
- B.2.1 One Degree ol Freedom Hamiltonian Systems
- B.2.2 Two Degrees ol Freedom Systems
- Problems
- C. A Fourth-Order Runge-Kutta Integration Method
- Problems
- Problems
- E. Fractals and Multifractals
- Problems
- Problems
- G. Inverse Scattering Transform for the Schrödinger Spectral Problem
- G.l The Linear Eigenvalue Problem
- G.2 The Direct Scattering Problem
- G.3 The Inverse Scattering Problem
- G.4 Reconstruction of the Potential
- Problems
- H. Inverse Scattering Transform for the Zakharov-Shabat Eigenvalue Problem
- H.1 The Linear Eigenvalue Problem
- H.2 The Direct Scattering Problem
- H.3 Inverse Scattering Problem
- H.4 Reconstruction of the Potentials
- Problems
- I. Integrable Discrete Soliton Systems
- I.1 Integrable Finite Dimensional N-Particles System on a Line: Calogero-Moser System
- I.2 The Toda Lattice
- I.3 Other Discrete Lattice Systems
- I.4 Solitary Wave (Soliton) Solution of the Toda Lattice
- Problems
- J. Painlevé Analysis for Partial Differential Equations
- J.1 The Painlevé Property for PDEs
- J.1.1 Painlevé Analysis
- J.2 Examples
- J.2.1 KdV Equation
- J.2.2 The Nonlinear Schrödinger Equation
- Problems
- References.