Results 21 to 30 of about 80,124 (249)
Integral Series Solution of the SchrÖdinger Equation for the Helium Atom
Physical Review Letters, 1967 Rapidly converging analytic solution by integral series of nonrelativistic Schroedinger equation for He ...
Brown, W. Byers, White, Ronald
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The HELP inequality on trees [PDF]
, 2008 We establish analogues of Hardy and Littlewood's integro-differential equation for Schrödinger-type operators on metric and discrete trees, based on a generalised strong limit-point property of the graph ...
Brown, B. Malcolm +2 more
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Numerical verification of a gap condition for a linearized nonlinear Schrödinger equation [PDF]
Nonlinearity, 2006 We make a detailed numerical study of the spectrum of two Schr¨ odinger operators L± arising from the linearization of the supercritical nonlinear Schr¨ odinger equation (NLS) about the standing wave, in three dimensions. This study was motivated by a recent result of the second author on the conditional asymptotic stability of solitary waves in the ...
Demanet, Laurent, Schlag, Wilhelm
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Discrete Fourier restriction associated with Schrödinger equations [PDF]
Revista Matemática Iberoamericana, 2014 We present a novel proof on the discrete Fourier restriction. The proof recovers Bourgain's level set result for Strichartz estimates associated with Schrödinger equations on a torus. Some sharp estimates on L^{{2(d+2)}/{d}} norms of certain exponential sums in higher dimensional cases ...
Hu, Yi, Li, Xiaochun
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Solving the Schrödinger equation with use of 1/N perturbation theory [PDF]
, 1984 The large N expansion provides a powerful new tool for solving the Schrödinger equation. In this paper, we present simple recursion formulas which facilitate the calculation.
Mlodinow, Leonard D., Shatz, Michael P.
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Spacetime Numerical Techniques for the Wave and Schrödinger Equations
, 2000 The most common tool for solving spacetime problems using finite elements is based on semidiscretization: discretizing in space by a finite element method and then advancing in time by a numerical scheme. Contrary to this standard procedure, in this dissertation we consider formulations where time is another coordinate of the domain.
Sepùlveda Salas, Paulina Ester
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Instability of standing waves of the Schrödinger equation with inhomogeneous nonlinearity [PDF]
Transactions of the American Mathematical Society, 2005 This paper is concerned with the inhomogeneous nonlinear Shrodinger equation (INLS-equation)iu_t + Δu + V(Єx)│u│^pu = 0, x Є R^N. In the critical and supercritical cases p ≥ 4/N, with N ≥ 2, it is shown here that standing-wave solutions of (INLS-equation) on H^1(R^N) perturbation are nonlinearly unstable or unstable by blow-up under certain conditions ...
Liu, Yue, Wang, Xiao-Ping, Wang, Ke
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Similarity Solutions of the Nonlinear Schrödinger Equation
Journal of Mathematical Analysis and Applications, 1994 AbstractGeneral similarity solution of the nonlinear Schrödinger equation is obtained by using group-theoretic methods. Similarity solutions for several special cases are also found. Finally, a solitary wave solution of the (1 + 2)-dimensional nonlinear Schrödinger equation in deep water is derived.
Ramasami, E. K., Debnath, L.
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Multicomplex Wave Functions for Linear And Nonlinear Schrödinger Equations [PDF]
Advances in Applied Clifford Algebras, 2016 We consider a multicomplex Schrodinger equation with general scalar potential, a generalization of both the standard Schrodinger equation and the bicomplex Schrodinger equation of Rochon and Tremblay, for wave functions mapping onto \(\mathbb {C}_k\). We determine the equivalent real-valued system in recursive form, and derive the relevant continuity ...
Theaker, Kyle A., Van Gorder, Robert A.
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DNLS equation for large-amplitude solitons propagating in an arbitrary direction in a high-[beta] Hall plasma [PDF]
, 2002 The one-dimensional oblique propagation of magnetohydrodynamic waves with arbitrary amplitudes in a Hall plasma with isotropic pressure is studied under assumption that the plasma [beta] is large.
Ruderman, M.S.
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