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Formally Exact and Practically Useful Analytic Solution of Harmonium
ACS OmegaWe provide a novel exact analytic solution of harmonium with arbitrary Coulomb interaction strength, for ground as well as all the excited states, using our recently developed method for solving Schrödinger equations. By comparing three formally exact analytic representations of the wave function including the one that utilizes biconfluent Heun ...
Wenqing Yao, Zhiyuan Yin, Chen Li
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Exact analytical solution for an Israel–Stewart cosmology [PDF]
General Relativity and Gravitation, 2020 In this article we report a novel analytic solution for a cosmological model with a matter content described by a one component dissipative fluid, in the framework of the causal Israel-Stewart theory. Some physically well motivated analytical relations for the bulk viscous coefficient, the relaxation time and a bariotropic equation of state are ...
Norman Cruz +2 more
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Analytical and Numerical Simulations of a Delay Model: The Pantograph Delay Equation
Axioms, 2022 In this paper, the pantograph delay differential equation y′(t)=ay(t)+byct subject to the condition y(0)=λ is reanalyzed for the real constants a, b, and c. In the literature, it has been shown that the pantograph delay differential equation, for λ=1, is
Essam Roshdy El-Zahar, Abdelhalim Ebaid
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On an Exact Analytical Solution of the Boussinesq Equation [PDF]
Transport in Porous Media, 2000 A useful exact analytical solution of the Boussinesq equation is discussed and is the most general solution presently available, and in particular yields a solution for a finite aquifer. It provides insight into the physical processes arising during the exchange of water between an aquifer and a free body of water of varying height as an application ...
Parlange, JY +4 more
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New Exact Solutions of Burgers’ Equation Using Power Index Method
Discrete Dynamics in Nature and Society, 2022 In this article, we focus on the new exact solutions of Burger’s equation by using a new technique which is known as the power index method (PIM). In this method, we choose suitable indexes of independent variables and similarity transformation so that ...
Khalil Ahmad, Khudija Bibi
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Two effective methods for solving nonlinear coupled time-fractional Schrödinger equations
Alexandria Engineering Journal, 2023 The objective of this work is to implement two efficient techniques, namely, the Laplace Adomian decomposition method (LADM) and the modified generalized Mittag–Leffler function method (MGMLFM) on a system of nonlinear fractional partial differential ...
Ismail Gad Ameen +2 more
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Exact analytical solutions for ADAFs [PDF]
Monthly Notices of the Royal Astronomical Society, 2016 to appear in ...
Habibi, Asiyeh +2 more
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Exact Analytic Solution for a Ballistic Orbiting Wind [PDF]
The Astrophysical Journal, 2017 Abstract Much theoretical and observational work has been done on stellar winds within binary systems. We present a new solution for a ballistic wind launched from a source in a circular orbit. The solution is that of a single wind—no second wind is included in the system and the shocks that arise are those due to the orbiting wind ...
Francis P. Wilkin, Harry Hausner
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Analytical solutions of exact renormalization group equations [PDF]
Nuclear Physics B, 1996 We study exact renormalization group equations in the framework of the effective average action. We present analytical solutions for the scale dependence of the potential in a variety of models. These solutions display a rich spectrum of physical behaviour such as fixed points governing the universal behaviour near second order phase transitions ...
Tetradis, N., Litim, D. F.
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ExactPack: A python library of exact analytic solutions
SoftwareX, 2023 Verification of multi-physics simulation software against problems with known analytic or semi-analytic solutions is an important aspect of research into a wide variety of fields involving the motion of fluids, shock physics and other dynamic material properties.
Jasper Thrussell, Jim Michael Ferguson
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