Bücher von Boling Guo

Quantum hydrodynamics comes from superfluid, superconductivity, semiconductor and so on. Quantum hydrodynamic model describes Helium II superfluid, Bose-Einstein condensation in inert gas, dissipative perturbation of Hamilton-Jacobi system, amplitude and dissipative perturbation of Eikonal quantum wave and so on. Owing to the broad application of quantum hydrodynamic equations, the study of the quantum hydrodynamic equations has aroused the concern of more and more scholars. Based on the above facts, we collected and collated the data of quantum hydrodynamic equations, and studied the concerning mathematical problems.The main contents of this book are: the derivation and mathematical models of quantum hydrodynamic equations, global existence of weak solutions to the compressible quantum hydrodynamic equations, existence of finite energy weak solutions of inviscid quantum hydrodynamic equations, non-isentropic quantum Navier-Stokes equations with cold pressure, boundary problem of compressible quantum Euler-Poisson equations, asymptotic limit to the bipolar quantum hydrodynamic equations.

This book provides an up-to-date overview of mathematical theories and research results in non-Newtonian fluid dynamics. Related mathematical models, solutions as well as numerical experiments are discussed. Fundamental theories and practical applications make it a handy reference for researchers and graduate students in mathematics, physics and engineering. Contents Non-Newtonian fluids and their mathematical model Global solutions to the equations of non-Newtonian fluids Global attractors of incompressible non-Newtonian fluids Global attractors of modified Boussinesq approximation Inertial manifolds of incompressible non-Newtonian fluids The regularity of solutions and related problems Global attractors and time-spatial chaos Non-Newtonian generalized fluid and their applications

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 methodBacklund 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

This book explains mathematical theories of a collection of stochastic partial differential equations and their dynamical behaviors. Based on probability and stochastic process, the authors discuss stochastic integrals, Ito formula and Ornstein-Uhlenbeck processes, and introduce theoretical framework for random attractors. With rigorous mathematical deduction, the book is an essential reference to mathematicians and physicists in nonlinear science. Contents:PreliminariesThe stochastic integral and Ito formulaOU processes and SDEsRandom attractorsApplicationsBibliographyIndex

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. ContentsThe Research Process for Rogue WavesConstruction of Rogue Wave Solution by the Generalized Darboux TransformationConstruction of Rogue Wave Solution by Hirota Bilinear Method, Algebro-geometric Approach and Inverse Scattering MethodThe Rogue Wave Solution and Parameters Managing in Nonautonomous Physical Model

This book focuses on the theory of the Zakharov system in the context of plasma physics. Rather than attempting to examine every aspect of the Zakharov system in detail, it provides an effective road map to help readers access the frontier of studies on this system.