Generalized Klein-Gordon Equation Research Articles

Group classification of a family of generalized Klein-Gordon equations by the method of indeterminates

A method for the group classification of differential equations we recently proposed is applied to the classification of a family of generalized Klein-Gordon equations. Our results are compared with other classification results of this family of equations labelled by an arbitrary function. Some conclusions are drawn with regards to the effectiveness of the proposed method.

Periodic and soliton structures in a generalized Klein–Gordon equation with horizontal singular lines

Periodic and soliton structures in a generalized Klein–Gordon equation with horizontal singular lines

Electromagnetic interaction with the Klein–Gordon equation in the framework of GUP

In this work, according to the generalized uncertainty principle, we study the Klein–Gordon equation interacting with the electromagnetic field. The generalized Klein–Gordon equation is obtained in the presence of a scalar electric potential and a uniform magnetic field. Furthermore, we find the relation of the generalized energy–momentum in the presence of a scalar electric potential and a uniform magnetic field separately.

An elementary proof of the existence of monotone traveling waves solutions in a generalized Klein–Gordon equation

We analyze the existence and uniqueness of monotone traveling wavefront for a generalized nonlinear Klein–Gordon model using classical arguments of ordinary differential equations, with V(x) a potentials family containing the ϕ‐four potential and the sine‐Gordon‐type potential . Also for these specific potentials, we give estimations of their monotone kink and anti‐kink solutions.

Using a New Auxiliary Equation to Construct Abundant Solutions for Nonlinear Evolution Equations

In this paper, a new auxiliary equation method is proposed. Combined with the mapping method, abundant periodic wave solutions for generalized Klein-Gordon equation and Benjamin equation are obtained. They are new types of periodic wave solutions which are rarely found in previous studies. As m → 0 and m → 1, some new types of trigonometric solutions and solitary solutions are also obtained correspondingly. This method is promising for constructing abundant periodic wave solutions and solitary solutions of nonlinear evolution equations (NLEEs) in mathematical physics.

GUP effects on Hawking temperature in Riemann space-time

In this paper, the modified Hawking temperature of a static Riemann space-time is studied using the generalized Klein–Gordon equation and the generalized Dirac equation. Applying the Kerner–Mann quantum tunneling method, the modified Hawking temperatures for scalar particles and fermions that cross the event horizon of the black hole have been derived. We observe that the quantum gravity effects reduce the rise of thermal radiation temperature of the black hole.

广义Klein-Gordon方程的行波解

广义Klein-Gordon方程的行波解

CHRONOLOGICAL PRODUCTS, ENERGY-MOMENTUM TENSORS OF SCALAR FIELDS FOR PARTICLE GENERATIONS, AND INDEFINITE METRICS

The solutions of generalized Klein-Gordon equations are considered. The generalizations of the Klein-Gordon equation allow one to derive convergent integrals for the Green functions of these equations. The generalized equations are presented as products of the operators for the Klein-Gordon equation with different masses. The solutions of derived homogeneous equations (total fields) are sums of fields corresponding to particles with the same values of the spin, the electric charge, the parities, but with different masses. Such particles are grouped into the kinds (families, dynasties) with members which are the generations. The chronological products of the scalar fields for kinds of particles are obtained at arbitrary quantity of the generations. These chronological products are the causal Green functions of generalized Klein-Gordon equations. The Lagrangians for the generalized Klein-Gordon equations of arbitrary order are derived. These Lagrangians are used to obtain the energy-momentum tensors for the particle kinds at arbitrary quantity of generations. It is shown that the generalized Hamiltonians (for total fields) have got positive eigenvalues for all the generations. These results are derived with the use of the indefinite metrics.

Soliton solutions of a generalized Klein–Gordon equation with power-law nonlinearity via the first integral method

This paper studies solitary wave solutions of a generalized nonlinear Klein-Gordon (KG) equation with power-law nonlinearity via the so-called first integral method. Using the method, some soliton solutions of the equation are obtained. The method is hereby shown to be an efficient and reliable mathematical tool for solving many nonlinear evolution equations arising in a number of problems in science and engineering. undefined undefined Звуковая функция ограничена 200 символами Настройки : История : Обратная связь : Donate Закрыть

Quantum Gravity Effects on Hawking Radiation of Schwarzschild-de Sitter Black Holes

The correction of Hawking temperature of Schwarzschild-de Sitter (SdS) black hole is investigated using the generalized Klein-Gordon equation and the generalized Dirac equation by taking the quantum gravity effects into account. We derive the corrected Hawking temperatures for scalar particles and fermions crossing the event horizon. The quantum gravity effects prevent the rise of temperature in the SdS black hole. Besides correction of Hawking temperature, the Hawking radiation of SdS black hole is also investigated using massive particles tunneling method. By considering self gravitation effect of the emitted particles and the space time background to be dynamical, it is also shown that the tunneling rate is related to the change of Bekenstein-Hawking entropy and small correction term (1 + 2β m 2). If the energy and the angular momentum are taken to be conserved, the derived emission spectrum deviates from the pure thermal spectrum. This result gives a correction to the Hawking radiation and is also in agreement with the result of Parikh and Wilczek.

Meshless numerical analysis of a class of nonlinear generalized Klein–Gordon equations with a well-posed moving least squares approximation

• A meshless method is developed for some generalized Klein–Gordon equations. • A convergent iterative scheme is performed to tackle the nonlinearity. • Examples involving five kinds of nonlinear equations and solitons are given. • Numerical results indicate that the method is about second-order convergence in both time and space. This paper presents a meshless method for the numerical solution of a class of nonlinear generalized Klein–Gordon equations. In this method, a time discrete technique is first adopted to discretize the time derivatives, and then a well-posed moving least squares (WP-MLS) approximation using shifted and scaled orthogonal basis functions is developed to approximate the spatial derivatives. To deal with the nonlinearity, an iterative scheme is presented and the corresponding convergence is discussed theoretically. Numerical examples involving Klein–Gordon, Dodd–Bullough–Mikhailov, sine-Gordon, double sine-Gordon and sinh-Gordon equations, and line and ring solitons are provided to illustrate the performance and efficiency of the method.

Travelling wave solutions of generalized Klein–Gordon equations using Jacobi elliptic functions

This paper obtains exact travelling wave solutions of five various forms of the generalized nonlinear Klein–Gordon equations using Jacobi elliptic functions. Topological and non-topological soliton solutions are obtained as well as Jacobi elliptic function solutions. It is acquired constraint conditions for the existence of solitons.

A geometric description of Maxwell field in a Kerr spacetime

We consider the Maxwell field in the exterior of a Kerr black hole. For this system, we propose a geometric construction of generalized Klein–Gordon equation called Fackerell–Ipser equation. Our model is based on conformal Yano–Killing tensor (CYK tensor). We present non-standard properties of CYK tensors in the Kerr spacetime which are useful in electrodynamics.

Deformed Hamilton-Jacobi Equations and the Tunneling Radiation of the Higher-Dimensional RN-(A)dS Black Hole

In this paper, we derive the deformed Hamilton-Jacobi equations from the generalized Klein-Gordon equation and generalized Dirac equation. Then, we study the tunneling rate, Hawking temperature and entropy of the higher-dimensional Reissner-Nordstrom de Sitter black hole via the deformed Hamilton-Jacobi equation. Our results show that the deformed Hamilton-Jacobi equations for charged scalar particles and charged fermions have the same expressions. Besides, the modified Hawking temperatures and entropy are related to the mass and charge of the black hole, the cosmology constant, the quantum number of emitted particles, and the term of GUP effects β.

Comment on: “An observation on the periodic solutions to nonlinear physical models by means of the auxiliary equation with a sixth-degree nonlinear term” [Commun Nonlinear Sci Numer Simulat 2013;18:2177–2187

This article shows that all novel exact solutions in the commented paper are not admitted by the original generalized Klein–Gordon equation and active-dissipative dispersive media equation. In addition, we present general solutions of certain auxiliary equation with sixth-degree nonlinear term. Then, based on above general solutions, we find that five cases in their Table 1 is shown to be incorrect.

Soliton solutions of the generalized Klein–Gordon equation by using $$\left( \frac{G^{\prime }}{G}\right) $$ G ′ G -expansion method

The aim of this paper is to present solitary wave solutions of two different forms of Klein–Gordon equations with full nonlinearity. The $$\left( \frac{G'}{G}\right) $$ -expansion method is applied to solve the governing equations and then exact 1-soliton solutions are obtained. It is shown that this method provides us with a powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.

Exact multisoliton solutions of nonlinear Klein-Gordon equation in 1 + 2 dimensions

This paper studies the nonlinear generalized Klein-Gordon equation in 1 + 2 dimensions. Exact multisoliton solution of this equation is obtained for the case of quadratic-law nonlinearity by the formal linearization method. Subsequently, exact travelling wave solutions of the generalized forms of Klein-Gordon equations in 1 + 2 dimensions are established by the modification of the truncated expansion method.

An observation on the periodic solutions to nonlinear physical models by means of the auxiliary equation with a sixth-degree nonlinear term

It is a fact that in auxiliary equation methods, the exact solutions of different types of auxiliary equations may produce new types of exact travelling wave solutions to nonlinear equations. In this manner, various auxiliary equations of first-order nonlinear ordinary differential equation with distinct-degree nonlinear terms are examined and, by means of symbolic computation, the new solutions of original auxiliary equation of first-order nonlinear ordinary differential equation with sixth-degree nonlinear term are presented. Consequently, the novel exact solutions of the generalized Klein–Gordon equation and the active-dissipative dispersive media equation are found out for illustration purposes. They are also applicable, where conventional perturbation method fails to provide any solution of the nonlinear problems under study.

Blow-up of solutions of strongly dissipative generalized Klein–Gordon equations

We study the question of sufficient conditions for blow-up of solutions of a model initial-boundary value problem. We use a modified form of Levine's method to obtain sufficient conditions for blow-up in finite time.

Energy decay for a nonlinear generalized Klein-Gordon equation in exterior domains with a nonlinear localized dissipative term

We derive an energy decay estimate for solutions to the initial-boundary value problem of a semilinear wave equation in exterior domains with a nonlinear localized dissipation. Our equation includes an absorbing term like |u|αu, α ≥ 0, and can be regarded as a generalized Klein-Gordon equation at least if α is closed to 0. This observation plays an essential role in our argument.