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. ContentsIntroductionInverse
scattering transformAsymptotic behavior to initial value problems for some integrable evolution
nonlinear equationsInteraction of solitons and its asymptotic propertiesHirota methodBäcklund
transformations and the infinitely many conservation lawsMulti-dimensional solitons and their
stabilityNumerical computation methods for some nonlinear evolution equationsThe geometric
theory of solitonsGlobal existence and blow up for the nonlinear evolution equationsThe soliton
movements of elementary particles in nonlinear quantum fieldThe theory of soliton movement of
superconductive featuresThe soliton movements in condensed state systemsontents
