Abstract
The purpose of the book is a mathematical and experimental study of the circumstances that determine the occurrence of extreme multivalued waves, their evolution and description. The interdisciplinary nature of extreme waves is emphasized. It is known that Einstein tried to build a unified (interdisciplinary) field theory that would unite all interactions in Nature into a single system. The book uses this idea. The known equations of the scalar field are considered as the basis for the unification and description of extreme waves in the environment. This approach will allow us to raise fundamental questions about the many-valued, corpuscular-wave, nonlinear nature of the world around us. The idea that everything in the world obeys non-linear laws is illustrated. Various strongly non-linear wave processes are modeled, ranging from modeling the Euler figures and ocean waves to describing the birth of particle-waves and the Universe. It is shown that extreme waves model many patterns observed in liquid layers, optical systems, Bose-Einstein condensates, micro- and electronic resonators. Thus, the extreme waves discussed in this book can be applied to a variety of technologies and systems, from the atomic scale to space.
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