Invariant Measures for Stochastic Nonlinear Schr?dinger Equations, Jialin Hong; Xu Wang
Автор: Wu-Ming Liu; Emmanuel Kengne Название: Schr?dinger Equations in Nonlinear Systems ISBN: 9811365806 ISBN-13(EAN): 9789811365805 Издательство: Springer Рейтинг: Цена: 18167.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book explores the diverse types of Schr?dinger equations that appear in nonlinear systems in general, with a specific focus on nonlinear transmission networks and Bose–Einstein Condensates. In the context of nonlinear transmission networks, it employs various methods to rigorously model the phenomena of modulated matter-wave propagation in the network, leading to nonlinear Schr?dinger (NLS) equations. Modeling these phenomena is largely based on the reductive perturbation method, and the derived NLS equations are then used to methodically investigate the dynamics of matter-wave solitons in the network. In the context of Bose–Einstein condensates (BECs), the book analyzes the dynamical properties of NLS equations with the external potential of different types, which govern the dynamics of modulated matter-waves in BECs with either two-body interactions or both two- and three-body interatomic interactions. It also discusses the method of investigating both the well-posedness and the ill-posedness of the boundary problem for linear and nonlinear Schr?dinger equations and presents new results. Using simple examples, it then illustrates the results on the boundary problems. For both nonlinear transmission networks and Bose–Einstein condensates, the results obtained are supplemented by numerical calculations and presented as figures.
Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics is the first book to provide a systematic construction of exact solutions via linear invariant subspaces for nonlinear differential operators. Acting as a guide to nonlinear evolution equations and models from physics and mechanics, the book focuses on the existence of new exact solutions on linear invariant subspaces for nonlinear operators and their crucial new properties.
This practical reference deals with various partial differential equations (PDEs) and models that exhibit some common nonlinear invariant features. It begins with classical as well as more recent examples of solutions on invariant subspaces. In the remainder of the book, the authors develop several techniques for constructing exact solutions of various nonlinear PDEs, including reaction-diffusion and gas dynamics models, thin-film and Kuramoto-Sivashinsky equations, nonlinear dispersion (compacton) equations, KdV-type and Harry Dym models, quasilinear magma equations, and Green-Naghdi equations. Using exact solutions, they describe the evolution properties of blow-up or extinction phenomena, finite interface propagation, and the oscillatory, changing sign behavior of weak solutions near interfaces for nonlinear PDEs of various types and orders. The techniques surveyed in Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics serve as a preliminary introduction to the general theory of nonlinear evolution PDEs of different orders and types.
Автор: Michael Ruzhansky; Mitsuru Sugimoto; Jens Wirth Название: Evolution Equations of Hyperbolic and Schr?dinger Type ISBN: 303480802X ISBN-13(EAN): 9783034808026 Издательство: Springer Рейтинг: Цена: 13974.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Evolution equations of hyperbolic or more general p-evolution type form an active field of current research. The book gives an overview of a variety of ongoing current research in the field and, therefore, allows researchers as well as students to grasp new aspects and broaden their understanding of the area.
Автор: M. Nagasawa Название: Schr?dinger Equations and Diffusion Theory ISBN: 3034896840 ISBN-13(EAN): 9783034896849 Издательство: Springer Рейтинг: Цена: 6986.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
Schrodinger Equations and Diffusion Theory addresses the question "What is the Schrodinger equation?" in terms of diffusion processes, and shows that the Schrodinger equation and diffusion equations in duality are equivalent. In turn, Schrodinger's conjecture of 1931 is solved. The theory of diffusion processes for the Schrodinger equation tell us that we must go further into the theory of systems of (infinitely) many interacting quantum (diffusion) particles. The method of relative entropy and the theory of transformations enable us to construct severely singular diffusion processes which appear to be equivalent to Schrodinger equations. The theory of large deviations and the propagation of chaos of interacting diffusion particles reveal the statistical mechanical nature of the Schrodinger equation, namely, quantum mechanics. The text is practically self-contained and requires only an elementary knowledge of probability theory at the graduate level.
Описание: In this monograph the authors present detailed and pedagogic proofs of persistence theorems for normally hyperbolic invariant manifolds and their stable and unstable manifolds for classes of perturbations of the NLS equation, as well as for the existence and persistence of fibrations of these invariant manifolds.
Описание: In this monograph the authors present detailed and pedagogic proofs of persistence theorems for normally hyperbolic invariant manifolds and their stable and unstable manifolds for classes of perturbations of the NLS equation, as well as for the existence and persistence of fibrations of these invariant manifolds.
Автор: Catherine Sulem; Pierre-Louis Sulem Название: The Nonlinear Schr?dinger Equation ISBN: 1475773072 ISBN-13(EAN): 9781475773071 Издательство: Springer Рейтинг: Цена: 20962.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Filling the gap between the mathematical literature and applications to domains, the authors have chosen to address the problem of wave collapse by several methods ranging from rigorous mathematical analysis to formal aymptotic expansions and numerical simulations.
Автор: Masao Nagasawa Название: Schr?dinger Equations and Diffusion Theory ISBN: 3034805594 ISBN-13(EAN): 9783034805599 Издательство: Springer Рейтинг: Цена: 10480.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Self-contained and structurally coherent, this introduction to the theory and applications of diffusion processes deploys them to analyze Schrodinger`s equations, using relative entropy and the theory of transformations to forge apparently identical processes.
Автор: Micka?l D. Chekroun; Honghu Liu; Shouhong Wang Название: Approximation of Stochastic Invariant Manifolds ISBN: 3319124951 ISBN-13(EAN): 9783319124957 Издательство: Springer Рейтинг: Цена: 6986.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This first volume is concerned with the analytic derivation of explicit formulas for the leading-order Taylor approximations of (local) stochastic invariant manifolds associated with a broad class of nonlinear stochastic partial differential equations.
Описание: Focuses on both continuous and discontinuous one-dimensional piecewise-linear maps and summarizes the results related to bifurcation structures in regular and robust chaotic domains.
Автор: Serafin Fraga; Jose M. Garcia de la Vega; Eric S. Название: The Schr?dinger and Riccati Equations ISBN: 3540651055 ISBN-13(EAN): 9783540651055 Издательство: Springer Рейтинг: Цена: 14365.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The linear Schroedinger equation is central to Quantum Chemistry. The Riccati equation is used to study the one-dimensional Schroedinger equation. The authors develop the Schroedinger-Riccati equation as an approach to determine solutions of the time-independent, linear Schroedinger equation.
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