New Approaches to Nonlinear Waves

- 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