![nonlinear schrodinger equation nonlinear schrodinger equation](https://image2.slideserve.com/4443962/nonlinear-schr-dinger-equation-derivation-from-dispersion-relation5-l.jpg)
The set of such solutions on the ring is described by the C n character tables from the theory of point groups. Under periodic boundary conditions we find several classes of solutions: constant amplitude solutions corresponding to boosts of the condensate the nonlinear version of the well-known particle-on-a-ring solutions in linear quantum mechanics nodeless, real solutions and a novel class of intrinsically complex, nodeless solutions. Under box boundary conditions the solutions are the bounded analog of bright solitons on the infinite line, and are in one-to-one correspondence with particle-in-a-box solutions to the linear Schrodinger equation. Our solutions take the form of stationary trains of bright silitons. 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.In this second of two papers, we present all stationary solutions of the nonlinear Schrodinger equation with box of periodic boundary conditions for the case of attractive nonlinearity. He is an applied mathematician, and a Professor at the Department of Computer Science and Engineering, University of Quebec at Outaouais, Canada. degree in Physicomathematical Sciences from the Kharkiv State University (now Kharkiv National University), Ukraine in January 1994. His research interests include atomic and molecular physics and quantum optics theory, the theory of quantum information and quantum computation, and condensed matter theoryĮmmanuel Kengne obtained his Ph.D. 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.
#NONLINEAR SCHRODINGER EQUATION FULL#
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.
![nonlinear schrodinger equation nonlinear schrodinger equation](https://d3i71xaburhd42.cloudfront.net/81e7a33ecec36c93ea9ded8163431f037496696b/27-Figure2.1-1.png)
degree from the Institute of Metal Research, Chinese Academy of Sciences, Shenyang, China in June 1994. For both nonlinear transmission networks and Bose–Einstein condensates, the results obtained are supplemented by numerical calculations and presented as figures.
![nonlinear schrodinger equation nonlinear schrodinger equation](https://i.ebayimg.com/images/g/xbIAAOSwm7Jfa3t4/s-l300.jpg)
Using simple examples, it then illustrates the results on the boundary problems. It also discusses the method of investigating both the well-posedness and the ill-posedness of the boundary problem for linear and nonlinear Schrödinger equations and presents new results. 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. 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 nonlinear transmission networks, it employs various methods to rigorously model the phenomena of modulated matter-wave propagation in the network, leading to nonlinear Schrödinger (NLS) equations.
![nonlinear schrodinger equation nonlinear schrodinger equation](https://i1.rgstatic.net/publication/230970907_An_integrable_generalization_of_the_nonlinear_Schrodinger_equation_on_the_half-line_and_solitons/links/53d14dc50cf2a7fbb2e63d57/largepreview.png)
This book explores the diverse types of Schrödinger equations that appear in nonlinear systems in general, with a specific focus on nonlinear transmission networks and Bose–Einstein Condensates.