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Nonlinear Klein-gordon And Schrodinger Systems: Theory And Applications

Nonlinear Klein-gordon And Schrodinger Systems: Theory And Applications
Author: Luis Vazquez
Publisher: World Scientific
Total Pages: 382
Release: 1996-06-20
Genre:
ISBN: 981454809X

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This is the first of two Euroconferences aimed at addressing the issues of Nonlinearity and Disorder. The 1995 Euroconference was devoted to the mathematical, numerical and experimental studies related to the Klein-Gordon and Schrödinger systems. The Euroconference was organized around main lectures in each area to introduce the main concepts and stimulate discussions. The mathematical studies covered the functional anlaysis and stochastic techniques applied to the general Klein-Gordon and Schrödinger wave equations. Also a panoramic view of the numerical schemes was presented to simulate the above equations, as well as an overview of the applications of such systems in the areas of condensed matter, optical physics, new materials and biophysics. Special attention was devoted to the discrete Schrödinger and Klein-Gordon systems and their applications.


Nonlinear Klein-Gordon and Schroedinger Systems

Nonlinear Klein-Gordon and Schroedinger Systems
Author: Luis Vázquez
Publisher: World Scientific Publishing Company Incorporated
Total Pages: 363
Release: 1996
Genre: Science
ISBN: 9789810225650

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Quantum Mechanics in Nonlinear Systems

Quantum Mechanics in Nonlinear Systems
Author: Xiao-Feng Pang
Publisher: World Scientific
Total Pages: 646
Release: 2005
Genre: Science
ISBN: 9812561161

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In the history of physics and science, quantum mechanics has served as the foundation of modern science. This book discusses the properties of microscopic particles in nonlinear systems, principles of the nonlinear quantum mechanical theory, and its applications in condensed matter, polymers and biological systems.The book is essentially composed of three parts. The first part presents a review of linear quantum mechanics, as well as theoretical and experimental fundamentals that establish the nonlinear quantum mechanical theory. The theory itself and its essential features are covered in the second part. In the final part, extensive applications of this theory in physics, biology and polymer are introduced. The whole volume forms a complete system of nonlinear quantum mechanics.The book is intended for researchers, graduate students as well as upper-level undergraduates.


Schrödinger Equations in Nonlinear Systems

Schrödinger Equations in Nonlinear Systems
Author: Wu-Ming Liu
Publisher: Springer
Total Pages: 569
Release: 2019-03-20
Genre: Science
ISBN: 9811365814

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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. 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. 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 Schrödinger 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.


Proceedings of the Workshop Nonlinear Physics, Theory and Experiment, II

Proceedings of the Workshop Nonlinear Physics, Theory and Experiment, II
Author: Mark J. Ablowitz
Publisher: World Scientific
Total Pages: 442
Release: 2003
Genre: Business & Economics
ISBN: 9789812704467

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Pt. I. Analytical methods. On the IST for discrete nonlinear Schrödinger systems and polarization shift for discrete vector solitons / M.J. Ablowitz, B. Prinari, A.D. Trubatch -- Soliton solutions of coupled nonlinear Klein-Gordon equations / T. Alagesan -- Characteristic initial value problems for integrable hyperbolic reductions of Einstein's equations / G.A. Alekseev -- Discrete sine-Gordon equation / M. Boiti [und weitere] -- Integrable and non-integrable equations with peakons / A. Degasperis, D.D. Holm, A.N.W. Hone -- Solution of a free boundary problem for a nonlinear diffusion-convection equation / S. De Lillo, M.C. Salvatori, G. Sanchini -- Iterative construction of solutions for a nonisospectral problem in 2 + 1 dimensions / P.G. Estevez -- Discrete breathers close to the anticontinuum limit: existence and wave scattering / S. Flach [und weitere] -- Complex Toda chain - an integrable universal model for adiabatic N-soliton interactions! / V.S. Gerdjikov -- On the reductions and scattering data for the generalized Zakharov-Shabat systems / G.G. Grahovski -- Bilinear representation for the modified nonlinear Schrödinger equations and their quantum potential deformations / J.H. Lee, O.K. Pashaev -- Noncommutative Burgers' equations / L. Martina, O.K. Pashaev -- On the quasi-classical [sumbol]-dressing method / B. Konopelchenko, A. Moro -- New solvable matrix integrals - U(n) case / A. Yu. Orlov -- Integrable hydrodynamic chains / M.V. Pavlov -- KPII: new results and open problems / A.K. Pogrebkov -- A workmate for KdV / P.C. Sabatier -- Space-time lattice for operator Schrödinger equation / A. Spire, V.V. Konotop, L. Vazquez -- On isomonodromy deformations for the ZS-AKNS flows / D. Wu -- pt. II. Symmetry properties, Hamiltonian methods and group theoretical methods. New symmetry reductions for a lubrication model / M.S. Bruzón [und weitere] -- Quantum solitons for quantum information and quantum computing / R.K. Bullough, M. Wadati -- Solving renormalization group equations by recursion relations / A. Cafarella, C. Corianò, M. Guzzi -- A tri-Hamiltonian route to spectral curves / L. Degiovanni, G. Magnano -- Construction of real forms of complexified Hamiltonian dynamical systems / V.S. Gerdjikov [und weitere] -- Integrable and super-integrable systems in classical and quantum mechanics / M. Giordano [und weitere] -- Non-commuting coordinates in vortex dynamics and in the Hall effect, related to "exotic" Galilean symmetry / P.A. Horváthy -- Structure of multi-meron knot action / L.S. Isaev, A.P. Protogenov -- Compatible nonlocal Poisson brackets of hydrodynamic type and integrable reductions of the Lamé equations / O.I. Mokhov -- Pseudoanti-Hermiticity in QQM, time-reversal and Kramers degeneracy / G. Scolarici -- On the integrability of supersymmetric equations / P. Tempesta, R.A. Leo, G. Soliani


Nonlinear Partial Differential Equations for Scientists and Engineers

Nonlinear Partial Differential Equations for Scientists and Engineers
Author: Lokenath Debnath
Publisher: Springer Science & Business Media
Total Pages: 602
Release: 2013-11-11
Genre: Mathematics
ISBN: 1489928464

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This expanded and revised second edition is a comprehensive and systematic treatment of linear and nonlinear partial differential equations and their varied applications. Building upon the successful material of the first book, this edition contains updated modern examples and applications from diverse fields. Methods and properties of solutions, along with their physical significance, help make the book more useful for a diverse readership. The book is an exceptionally complete text/reference for graduates, researchers, and professionals in mathematics, physics, and engineering.