The book is devoted to several topical questions in modern mathematical and theoretical physics, astrophysics, geophysics, and cosmology that remain unsolved within the framework of the standard approaches. To them, one can attribute unexplained properties of the magnetic fields of stars and planets, puzzles of the Earth's atmosphere, the phenomenon of ball lightning, the problem of a qualitative description for nuclear forces and their well-known property of saturation, enigmatic properties of spiral galaxies, the problem of the cosmological singularity, mysteries of the dark matter and dark energy, amongst others. To find theoretical ways for understanding such phenomena, new nonlinear generalizations of the classical field theories and advanced methods to solve nonlinear equations arising in them are studied and presented in this book.

Contents:

• Introduction
• Yang–Mills Theory and Anomalous Physical Phenomena
• Peculiar Interactions in Yang–Mills Fields
• Nonlinear Waves in Yang–Mills Fields
• Nonlinear Nuclear Interactions
• Relativistic Quantum Equations for Nucleons and Light Atomic Nuclei
• New Approaches in General Relativity
• Weyl's Principle of Scale Invariance and a New Cosmology

Readership: Advanced undergraduate and graduate students, physicists, astrophysicists and mathematicians interested in nonlinear field theories and their applications to unsolved problems of contemporary mathematical physics and theoretical physics, astrophysics, cosmology and the explanations of the mysterious phenomena in nature.

Key Features:

• The nonlinear generalizations of the classical field theories proposed in the book are new and based on fundamental principles of theoretical physics
• It is shown that these nonlinear generalizations can play an important role to explain some mysterious phenomena in nature
• The book is essential reading for anyone interested in nonlinear field theories and their applications to unsolved problems of contemporary mathematical and theoretical physics, astrophysics and cosmology