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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.
The monograph is devoted to a number of poorly explored problems of
non-linear electrodynamics, nuclear physics, and general relativity
that are very important for astrophysics, geophysics, and
cosmology. In it new theoretical methods are proposed to solve the
problems under consideration and to explain a number of puzzling
experimental and observational data In the book the authors study
the non-linear equations of the Yang-Mills theory and their
applications to several unsolved problems of electrodynamics. They
find and investigate a non-linear generalisation of the Yukawa
meson theory to describe the phenomenon of nuclear saturation and
various properties of nuclei. They propose a generalised Dirac's
equation to describe the quark structure and anomalous magnetic
moments of nucleons. They consider a number of unsolved problems of
general relativity and study anomalous properties of gravitational
waves. Finally, they find and investigate a generalisation of the
Einstein gravitational equations based on Weyl's geometry to
explain puzzling properties of spiral galaxies and to apply it to
several unsolved problems of cosmology.
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