We obtain exact solutions of both angular and radial parts of the kleingordon equation in this spacetime, which are given in terms of the confluent heun functions. Shape invariance approach to exact solutions of the klein. Solutions of the klein gordon equation with generalized. These equations appear in the study of relativistic and quantum physics. It can be solved by means of inverse scattering method 1. A new class of exact solutions of the kleingordon equation of. Since the exact solution cannot be obtained explicitly for arbitrary timedependence of the eld, we discuss the asymptotic behavior of the solutions with the help of the relativistic. In this work, we solve the klein gordon kg equation for the general deformed morse potential with equal scalar and vector potentials by using the nikiforovuvarov nu method, which is based on the solutions of general secondorder linear. The exact energy eigenvalues and wavefunctions are derived analytically by using the nikiforov and uvarov method. Exact solutions of the kleingordon equation in the kerr. We obtain exact solutions of both angular and radial parts of the klein gordon equation in this spacetime, which are given in terms of the confluent heun functions. Exact solutions are presented of the kleingordon equation of a charged particle moving in a classical monochromatic electromagnetic plane wave in a medium of index of refraction nm. In the present work, the modified simplest equation method is used to construct exact solutions of the zakharov equations and the coupled klein gordon zakharov equations.

The results could find interesting applications in fields such as theoretical. In addition, the solutions of these wave equations are highly applicable in chemical physics and highenergy physics at higher spatial dimensions. It is secondorder in space and time and manifestly lorentzcovariant. Exact solutions of the massive kleingordonschwarzschild. Exact solutions of the kleingordon equation in the kerrnewman background and hawking radiation. Iii we separate variables and solve the kleingordon equation. In sec iv, using the algebraic method of separation of variables, we reduce the dirac equation to a system of rst order coupled di erential equations that we solve in terms of special functions. Two classes of explicit exact solutions hyperbolic and trigonometric solutions of the associated equations are characterized with some free parameters. The solutions obtained include solitons and periodic solutions. Gordon equation of the symmetric generalized woods. Based on the idea of the infinite series method, a simple and efficient method is proposed for obtaining exact solutions of nonlinear evolution equations. Exact solutions are presented of the kleingordon equation of a charged particle moving in a transverse monochromatic plasmon wave of arbitrary high amplitude, which propagates in an underdense plasma.

To make a comparison between numerical solutions and analytical ones, four klein gor don equations with quadratic or cubic nonlinearity are considered. We explore klein gordon equation in the new framework of quasihermitian quantum mechanics. Klein gordon kg equation is a basic relativistic wave equation that is well known to describe the motion of spin zero particles. Separation of variables and exact solution of the klein. It plays an important role to find the exact solutions of nonlinear evolution equations in the nonlinear problems. Exact solutions of sine gordon and multiple sine gordon equations are constructed in terms of solutions of a linear base equation, the klein gordon equation and also in terms of nonlinear base equations where the nonlinearity is polynomial in the dependent variable. New exact traveling wave solutions for the zakharov. Citeseerx document details isaac councill, lee giles, pradeep teregowda. The solutions of this equation are expressed in terms of hyperbolic, trigonometric, exponential and rational functions.

Exact solutions of the kleingordon equation in the. Exact solutions of the massdependent klein gordon equation with the vector quarkantiquark interaction and harmonic oscillator potential m. Separation of variables and exact solutions of generalized. By this approach it was possible to find several exact invariant solutions for the klein gordon equation uxx utt ku. The general solution to the klein gordon equation would then be given by. Exact solutions of the kleingordon equation with hylleraas potential article pdf available in fewbody systems 5334 december 2011 with 208 reads how we measure reads. Exact traveling wave solutions of the perturbed klein. We present the exact solution of the klein gordon with hylleraas potential using the nikiforovuvarov method. The potentials we consider here depend linearly on energy and inversely on the hyperradius. We obtain explicitly the bound state energy eigenvalues and the corresponding eigen function for swave.

Exact solutions of nonlinear evolution equations nlees play a vital role to reveal the internal mechanism of complex physical phenomena. Pdf exact solutions of the kleingordon equation with. New exact traveling wave solutions for the nonlinear klein. Some exact solutions for a klein gordon equation according to 8, and 9, in the last four decades the range of applica tion of lie theory deals among others with the following topics. Exact solutions of the kleingordon equation 179 substituting eq. Ita 2 1 theoretical physics group, department of physics, university of uyonigeria. Employing a transformation to hyperbolic space, we derive in a simple way exact solutions for the klein gordon equation in an infinite squarewell potential with one boundary moving at constant velocity, for the massless as well as for the massive case. Pdf exact solutions of the zoomeron and kleingordon. Pdf some exact solutions for a klein gordon equation. Therefore, a system that can be described by a complex solution to the klein gordon equation also be described by a system of two independent particles with equal mass that have real solutions to the klein klein gordon equation.

This work considers the influence of the gravitational field produced by a charged and rotating black hole kerrnewman spacetime on a charged massive scalar field. As a result, some exact solutions to the bulloughdodd equation, liouville equation, sine gordon equation and sinh gordon equation are obtained. Suppose w wx,t is a solution of the nonlinear kleingordon equation. Finally, the conclusions will be given in section 5.

Exact solutions of the kleingordon equation with hylleraas potential akpan n. We solve the klein gordon and dirac equations in an open cosmological universe with a partially horn topology in the presence of a time dependent magnetic eld. A symmetry group interpretation of the known results concerning separation of variables with the scalar klein gordon equation is also given. Exact solutions of the symmetric regularized long wave. Recently, a number of methods have proposed, such as the socalled tanhmethod 1, the homogeneous balance method 2 and so on. A method for generating exact solutions of the nonlinear. Pdf exact solutions of the kleingordon equation in the. The purpose of this paper is to present a class of particular solutions of a c2,1 conformally invariant nonlinear klein gordon equation by symmetry reduction. Exact solutions of a nonlinear kleingordon equation in. Section 3 is devoted to symmetry reductions of ordinary di.

By using this method, we obtain abundant new types of exact traveling wave solutions. The general solutions found, could be used for future explorations on the study for. Numerical solution of nonlinear kleingordon equation. Exact travelling wave solutions of the coupled klein. From the radial solution, we obtain the exact wave solutions near the exterior horizon of the black hole, and discuss the hawking radiation of charged massive scalar particles. The solutions obtained depend on two arbitrary functions and are in the form of running waves. Abstract exact solutions of nonlinear evolution equations nlees play a vital role to reveal the internal mechanism of complex physical phenomena. Shape invariance approach to exact solutions of the klein gordon equation t. We calculate the corresponding eigenfunctions and eigenvalues of this system by using the nikiforovuvarov method. A continuous, onecomplexparameter family pair of solutions of the klein gordon equation for a massive particle in schwarzschild spacetime, given in terms of elementary functions, is derived.

The local equilibrium distribution function and the amending function are obtained. It is a quantized version of the relativistic energymomentum relation. How to derive general solution to the klein gordon equation a. In section 4, the exact analytic solutions to the equation are investigated by means of the tanhcoth method. This method not very well known and used is of great importance in the scientific community. Solutions to common problems with probability interpretation and inde. In the first, wu and cai showed that the radial and angular equations. Exact solutions are presented of the klein gordon equation of a charged particle moving in a classical monochromatic electromagnetic plane wave in a medium of index of refraction nm 1. Exact solutions of nonlinear generalizations of the klein. A simple method for generating the exact solutions of the nonlinear klein gordon equation is proposed. The wave functions obtained are expressed in terms of jacobi polynomials. Solutions to the kleingordon equation for a charged massive scalar field in the kerr newman spacetime were obtained by wu and cai 12, and furuhashi and nambu.

We study the ddimensional klein gordon equation for a particle in a hypersphericallysymmetric potential. The onedimensional klein gordon equation for the massdependent generalized woodssaxon potential with equal scalar and vector potentials are studied in this paper. Approximate symmetry and exact solutions of the perturbed. We obtain a class of particular solutions of a c2,1 conformally invariant nonlinear klein gordon equation by symmetry reduction. Solutions of the kleingordon equation in an infinite. Exact solutions of the klein gordon equation in the presence of a dyon, magnetic flux and scalar potential in the specetime of gravitational defects a. The general solutions found, could be used for future explorations on. The lie symmetry method allows to find invariant solutions under certain groups of transformations for differential equations. Using the subgroups of similitude group reduced ordinary differential equations of second order and their solutions by a singularity analysis are classified. In this work, we solve the kleingordon kg equation for the general deformed morse potential with equal scalar and vector potentials by using the nikiforovuvarov nu method, which is based on the solutions of general secondorder linear. Exact solutions of ddimensional kleingordon equation. The obtained results include new soliton and periodic solutions. The lie symmetry approach along with the simplest equation and expfunction methods are used to obtain solutions of the symmetric regularized long wave equation, while the travelling wave hypothesis approach along with the simplest equation method is utilized to obtain new exact solutions of the klein gordon zakharov equations. Using the subgroups of similitude group reduced ordinary differential equations of second order and their solutions by a.

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