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Covers the high-frequency analysis of nonlinear Schrodinger equations in the presence of an external potential. This book consists of two relatively independent parts: WKB analysis, and caustic crossing. It also covers applications of WKB analysis to functional analysis, in particular to the Cauchy problem for nonlinear Schrodinger equations.

Schrödinger equation. --- Nonlinear theories. --- Nonlinear problems --- Nonlinearity (Mathematics) --- Calculus --- Mathematical analysis --- Mathematical physics --- Equation, Schrödinger --- Schrödinger wave equation --- Differential equations, Partial --- Particles (Nuclear physics) --- Wave mechanics --- WKB approximation --- Schrodinger equation.

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This book constitutes the first effort to summarize a large volume of results obtained over the past 20 years in the context of the Discrete Nonlinear Schrödinger equation and the physical settings that it describes. It contains an introduction to the model, its systematic derivation and its connection to applications, a subsequent analysis of the existence and the stability of fundamental nonlinear structures in 1, 2 and even 3 spatial lattice dimensions. It also covers the case of defocusing nonlinearities, the modulational instabilities of plane wave solutions, and the extension to multi-component lattices. In addition, it features a final chapter on special topics written by a wide array of experts in the field, addressing through short reviews, areas of particular recent interest.

Nonlinear systems. --- Nonlinear wave equations. --- Schrödinger equation. --- Equation, Schrödinger --- Schrödinger wave equation --- Differential equations, Partial --- Particles (Nuclear physics) --- Wave mechanics --- WKB approximation --- Wave equation --- Systems, Nonlinear --- System theory --- Quantum theory. --- Quantum Physics. --- Theoretical, Mathematical and Computational Physics. --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Quantum physics. --- Mathematical physics. --- Physical mathematics --- Mathematics

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Quantum chemistry --- fysicochemie --- Schrodinger equation --- Equation, Schrödinger --- Schrödinger wave equation --- Differential equations, Partial --- Particles (Nuclear physics) --- Wave mechanics --- WKB approximation --- Chemistry, Quantum --- Chemistry, Physical and theoretical --- Quantum theory --- Excited state chemistry --- Molecular dynamics. --- Quantum chemistry. --- Schrödinger equation. --- Molecular dynamics --- Schrödinger equation --- Dynamics, Molecular --- Dynamics

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This book treats the Stark effect of a hydrogenic atom or ion in a homogeneous electric field. It begins with a thorough review of previous work in this field since 1926. After the Schrödinger equation has been separated with respect to time dependence, centre of mass motion and internal motion, followed by a discussion of its eigenfunctions, the exact development in time of the probability amplitude for a decaying state is obtained by means of a formula analogous to the Fock-Krylov theorem. From this formula one obtains by means of the phase-integral approximation generated from a particular

Stark effect. --- Optical spectroscopy. --- Quantum theory. --- Schrödinger equation. --- Equation, Schrödinger --- Schrödinger wave equation --- Differential equations, Partial --- Particles (Nuclear physics) --- Wave mechanics --- WKB approximation --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Spectroscopy, Optical --- Visible spectroscopy --- Spectrum analysis --- Electrooptics --- Spectral line broadening --- Schrodinger equation.

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This book provides a comprehensive treatment of the Gross-Pitaevskii equation with a periodic potential; in particular, the localized modes supported by the periodic potential. It takes the mean-field model of the Bose-Einstein condensation as the starting point of analysis and addresses the existence and stability of localized modes. The mean-field model is simplified further to the coupled nonlinear Schrödinger equations, the nonlinear Dirac equations, and the discrete nonlinear Schrödinger equations. One of the important features of such systems is the existence of band gaps in the wave transmission spectra, which support stationary localized modes known as the gap solitons. These localized modes realise a balance between periodicity, dispersion and nonlinearity of the physical system. Written for researchers in applied mathematics, this book mainly focuses on the mathematical properties of the Gross-Pitaevskii equation. It also serves as a reference for theoretical physicists interested in localization in periodic potentials.

Schrödinger equation. --- Gross-Pitaevskii equations. --- Localization theory. --- Categories (Mathematics) --- Homotopy theory --- Nilpotent groups --- Equations, Gross-Pitaevskii --- Nonlinear Schrödinger equations --- Schrödinger equations, Nonlinear --- Differential equations, Nonlinear --- Nonlinear wave equations --- Equation, Schrödinger --- Schrödinger wave equation --- Differential equations, Partial --- Particles (Nuclear physics) --- Wave mechanics --- WKB approximation