New Approaches to Nonlinear Waves

• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Άλλοι συγγραφείς: Tobisch, Elena (Επιμελητής έκδοσης)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2016.
• Σειρά: Lecture Notes in Physics, 908
• Θέματα: Physics.; Continuum physics.; Geophysics.; Statistical physics.; Dynamical systems.; Theoretical, Mathematical and Computational Physics.; Classical Continuum Physics.; Statistical Physics, Dynamical Systems and Complexity.; Geophysics and Environmental Physics.

The book details a few of the novel methods developed in the last few years for studying various aspects of nonlinear wave systems. The introductory chapter provides a general overview, thematically linking the objects described in the book. Two chapters are devoted to wave systems possessing resona...

Πίνακας περιεχομένων:

• Introduction (E. Tobisch)
• Brief historical overview
• Main notions
• Resonant interactions
• Modulation instability
• Frameworks
• Reality check
• References
• The effective equation method (Sergei Kuksin and Alberto Maiocchi)
• Introduction
• How to construct the effective equation
• Structure of resonances
• CHM: resonance clustering
• Concluding remarks
• References
• On the discovery of the steady-state resonant water waves (Shijun Liao, Dali Xu and Zeng Liu)
• Introduction
• Basic ideas of homotopy analysis method
• Steady-state resonant waves in constant-depth water
• Experimental observation
• Concluding remarks
• References
• Modulational instability in equations of KdV type (Jared C. Bronski, Vera Mikyoung Hur and Mathew A. Johnson)
• Introduction
• Periodic traveling waves of generalized KdV equations
• Formal asymptotics and Whitham’s modulation theory
• Rigorous theory of modulational instability
• Applications
• Concluding remarks
• References
• Modulational instability and rogue waves in shallow water models (R. Grimshaw, K. W. Chow and H. N. Chan)
• Introduction
• Korteweg-de Vries equations
•  Boussinesq model
• Hirota-Satsuma model
• Discussion
• References
• Hamiltonian framework for short optical pulses (Shalva Amiranashvili)
• Introduction
•  Poisson brackets
•  Pulses in optical fibers
•  Hamiltonian description of pulses
•  Concluding remarks
• References
• Modeling water waves beyond perturbations (Didier Clamond and Denys Dutykh)
• Introduction
• Preliminaries
• Variational formulations
• Examples
• Discussion
• References
• Quantitative Analysis of Nonlinear Water-Waves: a Perspective of an Experimentalist (Lev Shemer)
• Introduction
• The experimental facilities
• The Nonlinear Schrödinger Equation
• The Modified Nonlinear Schrödinger (Dysthe) Equation
• The Spatial Zakharov Equation
•  Statistics of nonlinear unidirectional water waves
• Discussion and Conclusions
• References.