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. 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. In the first, wu and cai showed that the radial and angular equations. Iii we separate variables and solve the kleingordon equation. 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. Using the subgroups of similitude group reduced ordinary differential equations of second order and their solutions by a. We obtain a class of particular solutions of a c2,1 conformally invariant nonlinear klein gordon equation by symmetry reduction. 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. Exact solutions of the kleingordon equation by modi. A symmetry group interpretation of the known results concerning separation of variables with the scalar klein gordon equation is also given.
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. Yasuk 1 1 department of physics, erciyes university, 38039 kayseri, turkey. Numerical solution of nonlinear kleingordon equation. Abstract exact solutions of nonlinear evolution equations nlees play a vital role to reveal the internal mechanism of complex physical phenomena. We calculate the corresponding eigenfunctions and eigenvalues of this system by using the nikiforovuvarov method. In section 4, the exact analytic solutions to the equation are investigated by means of the tanhcoth method. The obtained results include new soliton and periodic solutions. Exact travelling wave solutions of the coupled klein. A new class of exact solutions of the kleingordon equation of. Citeseerx document details isaac councill, lee giles, pradeep teregowda. The general solution to the klein gordon equation would then be given by. Exact solutions of nonlinear evolution equations nlees play a vital role to reveal the internal mechanism of complex physical phenomena. Section 3 is devoted to symmetry reductions of ordinary di. Exact solutions of the kleingordon equation in the.
We present the exact solution of the klein gordon with hylleraas potential using the nikiforovuvarov method. Exact solutions of nonlinear generalizations of the klein. The general solutions found, could be used for future explorations on the study for. 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. Ita 2 1 theoretical physics group, department of physics, university of uyonigeria. Exact solutions of ddimensional kleingordon equation. Exact solutions of the kleingordon equation in the presence of a dyon, magnetic flux and scalar potential in the specetime of gravitational defects a. Finally, the conclusions will be given in section 5. 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. Pdf exact solutions of the zoomeron and kleingordon. Pdf exact solutions of the kleingordon equation with. To make a comparison between numerical solutions and analytical ones, four klein gor don equations with quadratic or cubic nonlinearity are considered. Recently, a number of methods have proposed, such as the socalled tanhmethod 1, the homogeneous balance method 2 and so on. 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.
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. Exact solutions of the kleingordon equation in the kerr. It plays an important role to find the exact solutions of nonlinear evolution equations in the nonlinear problems. 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. 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. 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. These equations appear in the study of relativistic and quantum physics. 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. The solutions obtained depend on two arbitrary functions and are in the form of running waves. It can be solved by means of inverse scattering method 1. 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. 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.
Pdf exact solutions of the kleingordon equation in the. Shape invariance approach to exact solutions of the klein gordon equation t. Separation of variables and exact solutions of generalized. Based on the idea of the infinite series method, a simple and efficient method is proposed for obtaining exact solutions of nonlinear evolution equations. New exact traveling wave solutions for the zakharov. Exact solutions of the symmetric regularized long wave. A simple method for generating the exact solutions of the nonlinear klein gordon equation is proposed. 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. Pdf some exact solutions for a klein gordon equation. It is secondorder in space and time and manifestly lorentzcovariant. This method not very well known and used is of great importance in the scientific community. As a result, some exact solutions to the bulloughdodd equation, liouville equation, sine gordon equation and sinh gordon equation are obtained. 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.
The general solutions found, could be used for future explorations on. Klein gordon kg equation is a basic relativistic wave equation that is well known to describe the motion of spin zero particles. We explore klein gordon equation in the new framework of quasihermitian quantum mechanics. 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. 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. The first integral method was used to construct exact solutions of the zoomeron and klein gordon zakharov equations. Solutions of the kleingordon equation in an infinite. By this approach it was possible to find several exact invariant solutions for the klein gordon equation uxx utt ku. The solutions obtained include solitons and periodic solutions. 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. It is a quantized version of the relativistic energymomentum relation. Suppose w wx,t is a solution of the nonlinear kleingordon equation.
Exact traveling wave solutions of the perturbed klein. Shape invariance approach to exact solutions of the klein. In addition, the solutions of these wave equations are highly applicable in chemical physics and highenergy physics at higher spatial dimensions. Exact solutions of the kleingordon equation 179 substituting eq. We study the ddimensional klein gordon equation for a particle in a hypersphericallysymmetric potential. 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. The onedimensional klein gordon equation for the massdependent generalized woodssaxon potential with equal scalar and vector potentials are studied in this paper. The solutions are expressed in terms of ince polynomials, which form a doubly infinite set. The solutions of this equation are expressed in terms of hyperbolic, trigonometric, exponential and rational functions. 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. We obtain explicitly the bound state energy eigenvalues and the corresponding eigen function for swave.
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. Two classes of explicit exact solutions hyperbolic and trigonometric solutions of the associated equations are characterized with some free parameters. Solutions of the klein gordon equation with generalized. Gordon equation of the symmetric generalized woods. Exact solutions of the kleingordon equation with hylleraas potential akpan n. The wave functions obtained are expressed in terms of jacobi polynomials. Approximate symmetry and exact solutions of the perturbed.
The local equilibrium distribution function and the amending function are obtained. Solutions to common problems with probability interpretation and inde. A method for generating exact solutions of the nonlinear. New exact traveling wave solutions for the nonlinear klein. 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. Separation of variables and exact solution of the klein. How to derive general solution to the klein gordon equation a. Exact solutions of the massive kleingordonschwarzschild. Exact solutions of a nonlinear kleingordon equation in. The exact energy eigenvalues and wavefunctions are derived analytically by using the nikiforov and uvarov method. Exact solutions of the kleingordon equation in the kerrnewman background and hawking radiation. The potentials we consider here depend linearly on energy and inversely on the hyperradius. Exact solutions of the massdependent klein gordon equation with the vector quarkantiquark interaction and harmonic oscillator potential m. By using this method, we obtain abundant new types of exact traveling wave solutions.
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