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Artificial boundary condition for klein-gordon equation by constructing mechanics structure

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Theoretical & Applied Mechanics Letters 2023年第5期13卷 394-398页

作者： Pang Gang Zheng Zijun School of Mathematical Sciences Beihang UniversityBeijing 100191China College of Mechanical Engineering Chongqing University of TechnologyChongqing 400054China

An innovative local artificial boundary condition is proposed to numerically solve the Cauchy problem of the klein-gordon equation in an unbounded ***,the equation is considered as the axial wave prop-agation in a bar supported on a spring *** numerical model is then truncated by replacing the half-infinitely long bar with an equivalent mechanical *** effective frequency-dependent stiffness of the half-infinitely long bar is expressed as the sum of rational terms using Pade *** each term,a corresponding substructure composed of dampers and masses is ***,the equivalent mechan-ical structure is obtained by parallelly connecting these *** proposed approach can be easily implemented within a standard finite element framework by incorporating additional mass points and damper *** examples show that with just a few extra degrees of freedom,the proposed approach effec-tively suppresses artificial reflections at the truncation boundary and exhibits first-order convergence.

关键词： Artificial boundary condition Pade approximation Dispersive wave Spring-damper-mass system klein-gordon equation

Generalised tanh-shaped hyperbolic potential: klein–gordon equation's bound state solution

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Communications in Theoretical Physics 2023年第7期75卷 22-32页

作者： V H Badalov S V Badalov Institute for Physical Problems Baku State University1148 BakuAzerbaijan Theoretical Materials Physics Paderborn UniversityD-33098 PaderbornGermany Theoretical PhysicsⅦ University of BayreuthD-95440 BayreuthGermany

The development of potential theory heightens the understanding of fundamental interactions in quantum *** this paper,the bound state solution of the modified radial klein–gordon equation is presented for generalised tanh-shaped hyperbolic potential from the Nikiforov–Uvarov *** resulting energy eigenvalues and corresponding radial wave functions are expressed in terms of the Jacobi polynomials for arbitrary l *** is also demonstrated that energy eigenvalues strongly correlate with potential parameters for quantum *** particular cases,the generalised tanh-shaped hyperbolic potential and its derived energy eigenvalues exhibit good agreement with the reported ***,the rovibrational energies are calculated for three representative diatomic molecules,namely H2,HCl and *** lowest excitation energies are in perfect agreement with experimental ***,the potential model is displayed to be a viable candidate for concurrently prescribing numerous quantum systems.

关键词： klein-gordon equation hyperbolic potential Nikiforov-Uvarov method diatomic molecules

Exact solutions of the klein-gordon equation with ring-shaped oscillator potential by using the Laplace integral transform

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Chinese Physics B 2012年第7期21卷 108-112页

作者： Sami Ortakaya Institute of Natural and Applied Sciences Erciyes University

We present exact solutions for the klein gordon equation with a ring-shaped oscillator potential. The energy eigenvalues and the normalized wave functions are obtained for a particle in the presence of non-central oscillator potential. The angulm＂ functions are expressed in terms of the hypergeometric functions. The radial eigenfunetions have been obtained by using the Laplace integral transform. By means of the Laplace transform method, which is efficient and simple, the radial klein-gordon equation is reduced to a first-order differential equation.

关键词： ring-shaped oscillator klein-gordon equation Laplace integral transform bound states

GLOBAL SOLUTIONS AND FINITE TIME BLOW UP FOR DAMPED klein-gordon equation

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Acta Mathematica Scientia 2013年第3期33卷 643-652页

作者：徐润章丁云华 College of Science Harbin Engineering University

We study the Cauchy problem of strongly damped klein-gordon equation. Global existence and asymptotic behavior of solutions with initial data in the potential well are derived. Moreover, not only does finite time blow up with initial data in the unstable set is proved, but also blow up results with arbitrary positive initial energy are obtained.

关键词： klein-gordon equation strongly damped global solutions blow up

On Time-Splitting Pseudospectral Discretization for Nonlinear klein-gordon equation in Nonrelativistic Limit Regime

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Communications in Computational Physics 2014年第7期16卷 440-466页

作者： Xuanchun Dong Zhiguo Xu Xiaofei Zhao Beijing Computational Science Research Center Beijing 100084P.R.China Department of Mathematics National University of SingaporeSingapore 119076Singapore College of Mathematics Jilin UniversityChangchun 130012P.R.China

In this work,we are concerned with a time-splitting Fourier pseudospectral(TSFP)discretization for the klein-gordon(KG)equation,involving a dimensionless parameterε∈(0,1].In the nonrelativistic limit regime,the smallεproduces high oscillations in exact solutions with wavelength of O(ε^(−2))in *** key idea behind the TSFP is to apply a time-splitting integrator to an equivalent first-order system in time,with both the nonlinear and linear subproblems exactly integrable in time and,respectively,Fourier frequency *** method is fully explicit and time ***,we establish rigorously the optimal error bounds of a second-order TSFP for fixedε=O(1),thanks to an observation that the scheme coincides with a type of trigonometric *** the second task,numerical studies are carried out,with special effortsmade to applying the TSFP in the nonrelativistic limit regime,which are geared towards understanding its temporal resolution capacity and meshing strategy for O(ε^(−2))-oscillatory solutions when 0<ε≪*** suggests that the method has uniform spectral accuracy in space,and an asymptotic O(ε^(−2)D^(t2))temporal discretization error bound(Dt refers to time step).On the other hand,the temporal error bounds for most trigonometric integrators,such as the well-established Gautschi-type integrator in[6],are O(ε^(−4)D^(t2)).Thus,our method offers much better approximations than the Gautschi-type integrator in the highly oscillatory *** results,either rigorous or numerical,are valid for a splitting scheme applied to the classical relativistic NLS reformulation as well.

关键词： klein-gordon equation high oscillation time-splitting trigonometric integrator error estimate meshing strategy.

Bound states of klein-gordon equation and Dirac equation for ring-shaped non-spherical oscillator scalar and vector potentials

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Chinese Physics B 2005年第1期14卷 42-44页

作者：张学骜陈柯段正路 CollegeofAerospaceandMaterialsEngineering NationalUniversityofDefenceTechnologyChangsha410073China DepartmentofPhysics TsinghuaUniversityBeijing100084China

Solving the klein-gordon equation and Dirac equation with ring-shaped non-spherical oscillator gives the exact bound state wavefunction and energy equation, and the relations between non-relativistic Schrodinger equat... 详细信息

关键词： ring-shaped non-spherical oscillator klein-gordon equation Dirac equation bound state

Bound states of klein-gordon equation for double ring-shaped oscillator scalar and vector potentials

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Chinese Physics B 2005年第3期14卷 463-467页

作者：陆法林陈昌远孙东升 DepartmentofPhysics YanchengTeachers'CollegeYancheng224002China

In Spherical polar coordinates, double ring-shaped oscillator potentials have supersymmetry and shape invariance for θ and τ coordinates. Exact bound state solutions of klein-gordon equation with equal double ring-shaped oscillator scalar and vector potentials are obtained. The normalized angular wavefunction expressed in terms of Jacobi polynomials and the normalized radial wavefunction expressed in terms of the Laguerre polynomials are presented. Energy spectrum equations are obtained.

关键词： double ring-shaped oscillator potentials supersymmetry and shape invariance klein-gordon equation scalar and vector potentials bound states

Exact solutions of the klein-gordon equation with Makarov potential and a recurrence relation

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Chinese Physics B 2007年第7期16卷 1863-1867页

作者：张民仓王振邦 School of Physics and Information Technology Shaanxi Normal University Xi'an 710062 China

In this paper, the klein-gordon equation with equal scalar and vector Makaxov potentials is studied by the factorization method. The energy equation and the normalized bound state solutions are obtained, a recurrence relation between the different principal quantum number n corresponding to a certain angular quantum number l is established and some special cases of Makarov potential axe discussed.

关键词： Makarov potential klein-gordon equation bound state factorization method

Bound states of the klein-gordon equation for ring-shaped Kratzer-type potential

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Chinese Physics B 2004年第5期13卷 575-578页

作者：强稳朝 FacultyofScience Xi'anUniversityofArchitectureandTechnologyXi'an710055China

The exact normalized bound state wavefunctions and energy equations of klein-gordon equation with equal scalar and vector ring-shaped Kratzer-type potential have been obtained.

关键词： ring-shaped Kratzer-type potential klein-gordon equation bound-state