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Conservation law
About: Conservation law is a research topic. Over the lifetime, 17340 publications have been published within this topic receiving 493018 citations.
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TL;DR: The Hermiticity of the fractional Hamilton operator and the parity conservation law for fractional quantum mechanics are established and the energy spectra of a hydrogenlike atom and of a fractional oscillator in the semiclassical approximation are found.
Abstract: Some properties of the fractional Schrodinger equation are studied. We prove the Hermiticity of the fractional Hamilton operator and establish the parity conservation law for fractional quantum mechanics. As physical applications of the fractional Schrodinger equation we find the energy spectra of a hydrogenlike atom (fractional "Bohr atom") and of a fractional oscillator in the semiclassical approximation. An equation for the fractional probability current density is developed and discussed. We also discuss the relationships between the fractional and standard Schrodinger equations.
1,391 citations
Book•
27 Sep 1996
TL;DR: In this paper, the authors define and define nonlinear hyperbolic systems in one space dimension and define finite difference schemes for one-dimensional systems in the case of multidimensional systems.
Abstract: From the contents: Introduction: Definitions and Examples.- Nonlinear hyperbolic systems in one space dimension.- Gas dynamics and reaction flows.- Finite Difference Schemes for one-dimensional systems.- The case of multidimensional systems.- An Introduction to Boundary conditions.
1,386 citations
Book•
11 Aug 2005
TL;DR: In this article, Jacobi polynomials Gauss-type integration Collocation differentiation Co discontinuous expansion bases are used to simulate incompressible flows in one-dimensional expansion bases.
Abstract: Introduction Fundamental concepts in one dimension Multi-dimensional expansion bases Multi-dimensional formulations Diffusion equation Advection and advection-diffusion Non-conforming elements Algorithms for incompressible flows Incompressible flow simulations:verification and validation Hyperbolic conservation laws Appendices Jacobi polynomials Gauss-Type integration Collocation differentiation Co discontinuous expansion bases Characteristic flux decomposition References Index
1,278 citations
TL;DR: In this paper, a method of solution for the derivative nonlinear Schrodinger equation is presented, where the appropriate inverse scattering problem is solved and the one-soliton solution is obtained, as well as the infinity of conservation laws.
Abstract: A method of solution for the ’’derivative nonlinear Schrodinger equation’’ i q t =−q x x ±i (q*q 2) x is presented. The appropriate inverse scattering problem is solved, and the one‐soliton solution is obtained, as well as the infinity of conservation laws. Also, we note that this equation can also possess ’’algebraic solitons.’’
1,196 citations
TL;DR: A new approach to the stabilization of numerical schemes in magnetohydrodynamic processes in which the divergence errors are transported to the domain boundaries with the maximal admissible speed and are damped at the same time is developed.
1,194 citations