Lecture Notes in Physics

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 Schrodinger Equation.- The Modified Nonlinear Schrodinger (Dysthe) Equation.- The Spatial Zakharov Equation.- Statistics of nonlinear unidirectional water waves.- Discussion and Conclusions.- References.