This book provides an up-to-date overview of mathematical theories and research results on solitons, presenting related mathematical methods and applications as well as numerical experiments. Different types of soliton equations are covered along with their dynamical behaviors and applications from physics, making the book an essential reference for researchers and graduate students in applied mathematics and physics. Contents Introduction Inverse scattering transform Asymptotic behavior to initial value problems for some integrable evolution nonlinear equations Interaction of solitons and its asymptotic properties Hirota method Backlund transformations and the infinitely many conservation laws Multi-dimensional solitons and their stability Numerical computation methods for some nonlinear evolution equations The geometric theory of solitons Global existence and blow up for the nonlinear evolution equations The soliton movements of elementary particles in nonlinear quantum field The theory of soliton movement of superconductive features The soliton movements in condensed state systemsontents

This book provides a broad and complete introductions to the molecular structure, novel and anomalous properties, nonlinear excitations, soliton motions, magnetization, and biological effects of water. These subjects are described by both experimental results and theoretical analyses. These contents are very interesting and helpful to elucidate and explain the problem of "what is on earth water". This book contains the research results of the author and plenty of scientists in recent decades."Water: Molecular Structure and Properties" is self-contained and unified in presentation. It may be used as an advanced textbook by graduate students and even ambitious undergraduates in Physics and Biology. It is also suitable for the researchers and engineers in Physics, Biology and water science.

This book presents a complete review of the theory of nonlinear quantum mechanics and which differs totally from the original discipline of quantum mechanics as well as the studies the nature of microscopic particles under action of the nonlinear interactions in the systems; which give numerous new and interesting properties and rules of motions of the particles, such as wave-corpuscle duality and localization, and which discusses the applications of theory as relates to condensed matter, polymers, and biological systems. It is intended for researchers, teachers, graduate students and upper-level undergraduate students. The so-called discipline of nonlinear quantum mechanics (NLQM) is, in reality, only a theory for studying the properties and motion of microscopic particles (MIPs) in nonlinear physical systems. It was so named in relation to the concept of quantum mechanics established by Bohr, Heisenberg, Schrodinger and numerous others. The latter deals only with the properties and motion of microscopic particles in linear systems without nonlinear interactionh and will, here-in-after, referred to as linear quantum mechanics (LQM). The following topics are covered in 6 chapters i