The purpose of the book is a mathematical and experimental study of extreme, multivalued waves based on scalar field equations. 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, supplemented by the idea that all fundamental interactions have a wave, resonant, nonlinear nature. The theoretical foundation of the book also consists of the results of Leonard Euler.
Fundamental questions about the polysemy of Nature are considered. On this basis, various highly nonlinear wave processes are modeled, ranging from waves in resonators and ocean waves to descriptions of particle-waves, the origin of the Universe and data from double-slit experiments. Gravitational and inertial effects are associated with solutions of relativistic wave equations. According to the book, the unsolved nature of some fundamental problems in physics is explained by the nonlinear and resonant nature of the world around us, which exists in a non-smooth and inhomogeneous space-time.
We do not know how strong the influence of multivalued wave processes on the Universe is. This book is the first attempt to assess this influence. At the same time, the extreme waves considered in this book may be applied to different technologies and systems ranging from the atomic scale to the cosmos.
With this book, the author celebrates the 100th anniversary of the beginning of the development of quantum mechanics and modern cosmology.
Part I. From Euler figures to Faraday waves and particle-waves.
Chapter
1. Basic equations of scalar fields and examples of nonlinear waves arising
in them.
Chapter
2. Euler figures, unidirectional multivalued waves, quanta
and vortices.
Chapter
3. Waves in resonators: dAlembert method and
multivalued Faraday waves.
Chapter
4. Particle-waves and quanta in resonant
scalar fields, and classification of multivalued waves.- Part II. From
particle-waves to universes.
Chapter
5. Resonant scalar fields, appearance
of particles and galaxies.
Chapter
6. Nonlinear quantum waves in the light
of recent slit experiments.
Chapter
7. Model of eruption of the Universe out
of a pre-universe and its early evolution.
Chapter 8. Everything is
determined by everything.
Shamil Usmanovich Galiev was born on April 18, 1942 in Kazan, Tatar Republic (Russia) and is the son of Usman Zakirovich Galiev and his wife Ajar Khayrutdinovna Valitova. He was a researcher in the Academy Sciences of SSSR, Kazan in 19651972 and in Academy Sciences Ukraine, Kiev in 19721981, a head of the department in Academy Sciences Ukraine, Kiev in 19811995, a professor in Kiev Politech. U. in 19861989 and a visiting professor at Brown U., Providence in 1992. Since 1996, he has been a professor and honorary academician at the University of Auckland, New Zealand.
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