Schrödinger Equations in Nonlinear Systems
暫譯: 非線性系統中的薛丁格方程
Liu, Wu-Ming, Kengne, Emmanuel
- 出版商: Springer
- 出版日期: 2019-03-29
- 售價: $7,920
- 貴賓價: 9.5 折 $7,524
- 語言: 英文
- 頁數: 569
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 9811365806
- ISBN-13: 9789811365805
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商品描述
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.
商品描述(中文翻譯)
這本書探討了在非線性系統中出現的各種薛丁格方程，特別關注非線性傳輸網路和玻色-愛因斯坦凝聚體（Bose-Einstein Condensates, BECs）。在非線性傳輸網路的背景下，書中採用了多種方法來嚴謹地建模網路中調制物質波傳播的現象，導致非線性薛丁格（Nonlinear Schrödinger, NLS）方程的產生。這些現象的建模主要基於簡約擾動法，所導出的NLS方程隨後用於系統地研究網路中物質波孤子的動力學。在玻色-愛因斯坦凝聚體的背景下，書中分析了具有不同類型外部勢能的NLS方程的動力學特性，這些勢能控制著在具有雙體相互作用或同時具有雙體和三體原子間相互作用的BEC中調制物質波的動力學。書中還討論了研究線性和非線性薛丁格方程邊界問題的良好性和不良性的方法，並提出了新的結果。通過簡單的例子，書中說明了邊界問題的結果。對於非線性傳輸網路和玻色-愛因斯坦凝聚體，所獲得的結果都輔以數值計算並以圖形形式呈現。
作者簡介
Wu-Ming Liu obtained his Ph.D. degree from the Institute of Metal Research, Chinese Academy of Sciences, Shenyang, China in June 1994. He became an Associate Professor at the Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, China, in 1996, and has been a Full Professor at the Institute of Physics at the same Academy since 2002. He has served as an editorial board member for several international journals, including Scientific Reports, Journals of Physics: Communication, Frontiers of Physics, Journal of Atomic and Molecular Science, China Measurement and Test. His research interests include atomic and molecular physics and quantum optics theory, the theory of quantum information and quantum computation, and condensed matter theory
Emmanuel Kengne obtained his Ph.D. degree in Physicomathematical Sciences from the Kharkiv State University (now Kharkiv National University), Ukraine in January 1994. He is an applied mathematician, and a Professor at the Department of Computer Science and Engineering, University of Quebec at Outaouais, Canada. Emmanuel Kengne has made major contributions to a vast number of fields, including the theory of well-posedness boundary value problems for partial differential equations, wave propagation on nonlinear transmission lines, optical and heat solitons, nonlinear dynamical lattices, Ginzburg--Landau equations, Boson--Fermion models, bio-thermal physics, light propagation, thermal therapy for tumors, as well as many other mathematical fields.
作者簡介(中文翻譯)
劉無名於1994年6月在中國沈陽的中國科學院金屬研究所獲得博士學位。1996年，他成為中國科學院理論物理研究所的副教授，並自2002年起擔任該院物理研究所的正教授。他曾擔任多本國際期刊的編輯委員會成員，包括《Scientific Reports》、《Journals of Physics: Communication》、《Frontiers of Physics》、《Journal of Atomic and Molecular Science》和《China Measurement and Test》。他的研究興趣包括原子和分子物理學、量子光學理論、量子信息和量子計算理論，以及凝聚態物理理論。
艾曼紐·肯格尼於1994年1月在烏克蘭哈爾科夫國立大學（現為哈爾科夫國立大學）獲得物理數學科學博士學位。他是一位應用數學家，並擔任加拿大烏塔瓦大學計算機科學與工程系的教授。艾曼紐·肯格尼在多個領域做出了重大貢獻，包括偏微分方程的良定邊值問題理論、非線性傳輸線上的波傳播、光學和熱孤子、非線性動態晶格、金茲堡-朗道方程、玻色-費米模型、生物熱物理學、光傳播、腫瘤的熱療法，以及許多其他數學領域。
