Operational Solution to the Nonlinear Klein-Gordon Equation

We obtain solutions of the nonlinear Klein-Gordon equation using a novel operational method combined with the Adomian polynomial expansion of nonlinear functions. Our operational method does not use any integral transforms nor integration processes. We illustrate the application of our method by solving several examples and present numerical results that show the accuracy of the truncated series approximations to the solutions.     

A New Algebraic Method and Its Application to Nonlinear Klein-Gordon Equation

In terms of the solutions of the generalized Riccati equation, a new algebraic method, which contains the terms of radical expression of functions f（ξ）, is constructed to explore the new exact solutions for nonlinear evolution equations. Being concise and straightforward, the method is applied to nonlinear Klein-Gordon equation, and some new exact solutions of the system are obtained. The method is of important significance in exploring exact solutions for other nonlinear evolution equations.     

A New Algebraic Method and Its Application to Nonlinear Klein-Gordon Equation

In terms of the solutions of the generalized Riccati equation, a new algebraic method, which contains the terms of radical expression of functions f(ξ), is constructed to explore the new exact solutions for nonlinear evolution equations. Being concise and straightforward, the method is applied to nonlinear Klein-Gordon equation, and some new exact solutions of the system are obtained. The method is of important significance in exploring exact solutions for other nonlinear evolution equations.     

Perturbation Theory for Nonlinear Klein-Gordon Kinks

A direct approach is used to investigate perturbations about a kink solution for nonlinear Klein-Gordon models. Effects of perturbations on a kink are derived in this scheme. After linearizing the initial equations by making use of derivative expansion method from classical perturbation theory, the solution for the first-order correction is derived by means of the method of Laplace transformation. The parameter variations are naturally given by the secular conditions.     

Asymptotic Completeness for a Renormalized Nonrelativistic Hamiltonian in Quantum Field Theory: The Nelson Model

Scattering theory for the Nelson model is studied. We show Rosen estimates and we prove the existence of a ground state for the Nelson Hamiltonian. Also we prove that it has a locally finite pure point spectrum outside its thresholds. We study the asymptotic fields and the existence of the wave operators. Finally we show asymptotic completeness for the Nelson Hamiltonian.     

Exact Analytical Solution of the Klein-Gordon Equation in the Generalized Woods-Saxon Potential

The exact analytical solution of the Klein-Gordon equation for the spin-0 particles in the generalized Woods-Saxon potential is presented. The bound state energy eigenvalues and corresponding wave functions are obtained in the closed forms. The correlations between the potential parameters and energy eigenvalues are examined for π⁰ particles.     

New Doubly Periodic Solutions for the Coupled Nonlinear Klein-Gordon Equations

By using the general solutions of a new coupled Riccati equations, a direct algebraic method is described to construct doubly periodic solutions (Jacobi elliptic function solution) for the coupled nonlinear Klein-Gordon equations.It is shown that more doubly periodic solutions and the corresponding solitary wave solutions and trigonometric function solutions can be obtained in a unified way by this method.     

Multisymplectic Pseudospectral Discretizations for (3+1)-Dimensional Klein-Gordon Equation

We explore the multisymplectic Fourier pseudospectral discretizations for the (3+1)-dimensional Klein-Gordon equation in this paper. The corresponding multisymplectic conservation laws are derived. Two kinds of explicit symplectic integrators in time are also presented.     

一维Hulthén势场中Klein-Gordon粒子的透射共振

用Heaviside函数构造出一维对称的Hulthén势垒,求解了其满足的Klein-Gordon方程. 散射态的精确解可以由超几何函数表示, 透射系数T和反射系数R能由Klein-Gordon 方程满足的边界条件得到.并由流密度守恒推导出低动量粒子发生透射共振的条件. 关键词： Klein-Gordon方程 Hulthén势垒 散射态 透射共振     

A Novel Method to Solve Nonlinear Klein-Gordon Equation Arising in Quantum Field Theory Based on Bessel Functions and Jacobian Free Newton-Krylov Sub-Space Methods

The Klein-Gordon equation arises in many scientific areas of quantum mechanics and quantum field theory.In this paper a novel method based on spectral method and Jacobian free Newton method composed by generalized minimum residual(JFNGMRes) method with adaptive preconditioner will be introduced to solve nonlinear Klein-Gordon equation. In this work the nonlinear Klein-Gordon equation has been converted to a nonlinear system of algebraic equations using collocation method based on Bessel functions without any linearization, discretization and getting help of any other methods. Finally, by using JFNGMRes, solution of the nonlinear algebraic system will be achieved. To illustrate the reliability and efficiency of the proposed method, we solve some examples of the Klein-Gordon equation and compare our results with other methods.     

A Search on the Klein-Gordon Equation

The s-wave Klein-Gordon equation for the bound states is separated in two parts to see clearly the relativistic contributions to the solution in the non-relativistic limit. The reliability of the model is discussed with two examples chosen specifically.     

Approximate Solution of the Effective Mass Klein-Gordon Equation for the Hulthen Potential with Any Angular Momentum

The radial part of the effective mass Klein-Gordon equation for the Hulthen potential is solved by making an approximation to the centrifugal potential. The Nikiforov-Uvarov method is used in the calculations. Energy spectra and the corresponding eigenfunctions are computed. Results are also given for the case of constant mass.     

Quark potentials for mesons in the Klein-Gordon equation

Two relativistic potential models are applied to describe meson spectroscopy in a unified way, encompassing both light and heavy quark systems. A combination of linear and coulomb potentials has been investigated for Klein-Gordon equation using the WKB approximation. A power-like phenomenological potential model has also been studied in the Klein-Gordon framework. Meson masses calculated for both the potentials give a good agreement with the corresponding experimental values.     

一般Hartmann势Klein-Gordon方程的束缚态

用分离变量方法讨论了在一般Hartmann标量势和矢量势相等条件下Klein-Gordon方程的束缚态解.体系的性质与三个量子数及一般Hartmann势的势参数有关.给出了用广义连带勒让德多项式表示的归一化角向波函数和用合流超几何函数表示的归一化径向波函数,获得了精确的束缚态能谱方程.氢原子势、类氢原子势和Hartmann势是本文一般Hartmann势的三个特例.     

Phase Formulation and Exact Solutions for the Relativistic Klein-Gordon Field with a Time-Dependent Hamiltonian

On the basis of the phase formulation, we find the quantum and classical exact solutions and corresponding total phases for the Klein-Gordon (KG) field with a time-dependent Hamiltonian. The total phase includes both the dynamical and geometric phases (Abaronov-Anandan phase). The connection between the quantum and classical solutions is then obtained. From this connection, we discuss the condition under which the geometric phase for the KG field can be defined.     

Approximate analytical solutions of scattering states for Klein-Gordon equation with Hulthén potentials for nonzero angular momentum

In this paper, using the exponential function transformation approach along with an approximation for the centrifugal potential, the radial Klein-Gordon equation with the vector and scalar Hulthén potential is transformed to a hypergeometric differential equation. The approximate analytical solutions of t-waves scattering states are presented. The normalized wave functions expressed in terms of hypergeometric functions of scattering states on the “k/2π scale” and the calculation formula of phase shifts are given. The physical meaning of the approximate analytical solution is discussed.      

Klein-Gordon方程Q球解中能量稳定性和扰动研究

本文研究了一种复标量场模型中的双层Q球解,在解析形式下计算了Q球荷和能量. 同时,分析了其能量稳定性质,通过Klein-Gordon 方程获得了Q球能量的扰动表达式. 另外,还讨论了Q球暗物质产生的物理效应. 关键词： Klein-Gordon方程 Q球解 能量稳定性与扰动 暗物质