Schrцdinger Equations in Nonlinear Systems, Liu Wu-Ming, Kengne Emmanuel
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.
Описание: The study of attractors of dynamical systems occupies an important position in the modern qualitative theory of differential equations.
Автор: Sidorov Denis Название: Integral Dynamical Models: Singularities, Signals and Control ISBN: 9814619183 ISBN-13(EAN): 9789814619189 Издательство: World Scientific Publishing Цена: 12514.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This volume provides a broad introduction to nonlinear integral dynamical models and new classes of evolutionary integral equations.
Описание: This book describes the direct and inverse problems of the multidimensional Schroedinger operator with a periodic potential, a topic that is especially important in perturbation theory, constructive determination of spectral invariants and finding the periodic potential from the given Bloch eigenvalues.
Описание: Smooth theory in dimensions 2 and 3.- Standard Theory.- 2D degenerating magnetic Schrцdinger operator.- 2D magnetic Schrцdinger near boundary.- Magnetic Schrцdinger operator: short loops.- Dirac operator with strong magnetic field.
Описание: This book describes the direct and inverse problems of the multidimensional Schr?dinger operator with a periodic potential, a topic that is especially important in perturbation theory, constructive determination of spectral invariants and finding the periodic potential from the given Bloch eigenvalues. It provides a detailed derivation of the asymptotic formulas for Bloch eigenvalues and Bloch functions in arbitrary dimensions while constructing and estimating the measure of the iso-energetic surfaces in the high-energy regime. Moreover, it presents a unique method proving the validity of the Bethe–Sommerfeld conjecture for arbitrary dimensions and arbitrary lattices. Using the perturbation theory constructed, it determines the spectral invariants of the multidimensional operator from the given Bloch eigenvalues. Some of these invariants are explicitly expressed by the Fourier coefficients of the potential, making it possible to determine the potential constructively using Bloch eigenvalues as input data. Lastly, the book presents an algorithm for the unique determination of the potential. This updated second edition includes an additional chapter that specifically focuses on lower-dimensional cases, providing the basis for the higher-dimensional considerations of the chapters that follow.
Автор: Aktosun Tuncay, Weder Ricardo Название: Direct and Inverse Scattering for the Matrix Schrцdinger Equation ISBN: 3030384306 ISBN-13(EAN): 9783030384302 Издательство: Springer Рейтинг: Цена: 18167.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Authored by two experts in the field who have been long-time collaborators, this monograph treats the scattering and inverse scattering problems for the matrix Schroedinger equation on the half line with the general selfadjoint boundary condition.
Описание: Non-smooth theory and higher dimensions.- Irregular coefficients in dimensions 2, 3.- Full-rank case.- Non-full-rank case.- 4D-Schrцdinger with degenerating magnetic field.- 4D-Schrцdinger Operator with the strong magnetic field.- Eigenvalue asymptotics for Schrцdinger and dirac operators with the strong magnetic field.- Eigenvalue asymptotics: 2D case.- Eigenvalue asymptotics: 3D case.
Описание: The book aims to describe some recent progress in nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete).
Описание: With a pedagogic format ideal for graduate students, this text includes a wealth of examples focusing on solutions in dynamical systems theory that mirror those used in Lyapunov`s first method, tackling ordinary differential equations expressed as series form.
Автор: Boling Guo, Dongfen Bian, Fangfang Li, Xiaoyu Xi Название: Vanishing Viscosity Method: Solutions to Nonlinear Systems ISBN: 3110495287 ISBN-13(EAN): 9783110495287 Издательство: Walter de Gruyter Рейтинг: Цена: 26024.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
The book summarizes several mathematical aspects of the vanishing viscosity method and considers its applications in studying dynamical systems such as dissipative systems, hyperbolic conversion systems and nonlinear dispersion systems. Including original research results, the book demonstrates how to use such methods to solve PDEs and is an essential reference for mathematicians, physicists and engineers working in nonlinear science.
Contents: Preface Sobolev Space and Preliminaries The Vanishing Viscosity Method of Some Nonlinear Evolution System The Vanishing Viscosity Method of Quasilinear Hyperbolic System Physical Viscosity and Viscosity of Difference Scheme Convergence of Lax-Friedrichs Scheme, Godunov Scheme and Glimm Scheme Electric-Magnetohydrodynamic Equations References
Автор: Vieri Benci; Donato Fortunato Название: Variational Methods in Nonlinear Field Equations ISBN: 3319361228 ISBN-13(EAN): 9783319361222 Издательство: Springer Рейтинг: Цена: 11878.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The book analyzes the existence of solitons, namely of finite energy solutions of field equations which exhibit stability properties.
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