Evolution of Extreme Waves and Resonances

Shamil U. Galiev obtained his Ph.D. degree in Mathematics and Physics from Leningrad University in 1971, and, later, a full doctorate (ScD) in Engineering Mechanics from the Academy of Science of Ukraine (1978). He worked in the Academy of Science of former Soviet Union as a researcher, senior researcher, and department chair from 1965 to 1995. From 1984 to 1989, he served as a Professor of Theoretical Mechanics in the Kiev Technical University, Ukraine. Since 1996, he has served as Professor, Honorary Academic of the University of Auckland, New Zealand. Dr. Galiev has published approximately 90 scientific publications, and he is the author of seven books devoted to different complex wave phenomena. From 1965-2014 he has studied different engineering problems connected with dynamics and strength of submarines, rocket systems, and target/projectile (laser beam) systems. Some of these results were published in books and papers. During 1998-2017, he conducted extensive research and publication in the area of strongly nonlinear effects connected with catastrophic earthquakes, giant ocean waves and waves in nonlinear scalar fields. Overall, Dr. Galiev’s research has covered many areas of engineering, mechanics, physics, and mathematics.

• 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.

"Galiev presents a comprehensive theory of extreme waves—unexpectedly appearing and disappearing waves with large amplitudes—a topic gaining attention especially in the last 20 years. Fundamental ingredients in such waves are nonlinearities (geometric or material) and behavior near and past resonance (hence large amplitudes). The theory is applied to ocean waves and optical physics…Some important experiments are drawn from the literature (e.g., Euler's work on the elastica, Darwin's observations on tsunami)."J. Lambropoulos, Choice Reviews October 2021, USA