Nan Liu

Boling Guo

Yu-Feng Wang

Xiao-Feng Pang

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 Bäcklund 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

Solitons

Lixin Tian

Zhenya Yan

Liming Ling

This book gives an overview of the theoretical research on rogue waves and discusses solutions to rogue wave formation via the Darboux and bilinear transformations, algebro-geometric reduction, and inverse scattering and similarity transformations. Studies on nonlinear optics are included, making the book a comprehensive reference for researchers in applied mathematics, optical physics, geophysics, and ocean engineering. Contents The Research Process for Rogue Waves Construction of Rogue Wave Solution by the Generalized Darboux Transformation Construction of Rogue Wave Solution by Hirota Bilinear Method, Algebro-geometric Approach and Inverse Scattering Method The Rogue Wave Solution and Parameters Managing in Nonautonomous Physical Model

Mathematical Theory and Applications in Physics

Rogue Waves

Yu-Feng Wang

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