The theory of waves is generalized on cases of strongly nonlinear waves, multivalued waves, and particle–waves. The appearance of these waves in various continuous media and physical fields is explained by resonances and nonlinearity effects. Extreme waves emerging in different artificial and natural systems from atom scale to the Universe are explored. Vast amounts of experimental data and comparisons of them with the results of the developed theory are presented.

The book was written for graduate students as well as for researchers and engineers in the fields of geophysics, nonlinear wave studies, cosmology, physical oceanography, and ocean and coastal engineering. It is designed as a professional reference for those working in the wave analysis and modeling fields.


PART I. An Example of a Unified Theory of Extreme Waves. Chapter 1 Lagrangian Description of Surface Water Waves. Chapter 2 Euler’s Figures and Extreme Waves: Examples, Equations and Unified Solutions. PART II. Waves in Finite Resonators. Chapter 3 Generalization of the d’Alembert’s Solution for Nonlinear Long Waves. Chapter 4 Extreme Resonant Waves: A Quadratic Nonlinear Theory. Chapter 5. Extreme Resonant Waves: A Cubic Nonlinear Theory. Chapter 6 Spherical Resonant Waves. Chapter 7 Extreme Faraday Waves. PART III. Extreme Ocean Waves and Resonant Phenomena. Chapter 8 Long Waves, Green's Law and Topographical Resonance. Chapter 9 Modelling of a Tsunami Described by Charles Darwin and Coastal Waves. Chapter 10. Theory of Extreme (Rogue, Catastrophic) Ocean Waves. Chapter 11. Wind-Induced Waves and Wind-Wave Resonance. Chapter 12. Transresonant Evolution of Euler’s Figures into Vortices. PART IV. Modelling of Particle-Waves, Slit Experiments and the Extreme Waves in Scalar Fields. Chapter 13. Resonances, Euler Figures, and Particle-Waves. Chapter 14. Nonlinear Quantum Waves in the Light of Recent Slit Experiments. Chapter 15. Resonant Models of Origin of Particles and the Universe Due to Quantum Perturbations of Scalar Fields. Conclusion to Volume I.