The Discrete Nonlinear Schrd̲inger Equation Mathematical Analysis, Numerical Computations and Physical Perspectives /

• Main Author: Kevrekidis, Panayotis G. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009.
• Series: Springer Tracts in Modern Physics, 232
• Subjects: Physics.; Quantum theory.; Mathematical physics.; Quantum Physics.; Mathematical and Computational Physics.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-540-89199-4

This book constitutes the first effort to summarize a large volume of results obtained over the past 20 years in the context of the Discrete Nonlinear Schrd̲inger equation and the physical settings that it describes. It contains an introduction to the model, its systematic derivation and its connect...

Table of Contents:

• 1. General Introduction and Derivation of the DNLS Equation
• 2. The One-Dimensional Case
• 3. The Two-Dimensional Case
• 4. The Three-Dimensional Case
• 5. The Defocusing Case
• 6. Extended Solutions and Modulational Instability
• 7. Multi-Component Solitary Waves
• 8. Experimental Results Related to DNLS Equations
• 9. Numerical Methods for DNLS
• 10. The Dynamics of Unstable Waves
• 11. A Map Approach to Stationary Solutions of the DNLS Equation
• 12. Formation of Localized Modes in DNLS
• 13. Few-lattice-site Systems of Discrete Self-Trapping Equations
• 14. Surface Waves and Boundary Effects in DNLS Equations
• 15. Discrete Nonlinear Schrd̲inger Equations with Time-Dependent Coefficients
• 16. Exceptional Discretizations of the NLS
• 17. Solitary Wave Collisions
• 18. Related Models
• 19. DNLS with Impurities
• 20. Statistical Mechanics of DNLS
• 21. Traveling Solitary Waves in DNLS Equations
• Decay and Strichartz Estimates for DNLS.