Sinegordon equation is generally p osed as an initial alue v problem on r i for t 0. The given equation is decomposed into a system of equations and. It is based on the previous work, resonant structures within the nonlinear kleingordon equations, the thesis of dr. Representing the kernels of the marchenko equation in a separated form by using a suitable triplet of constant real matrices a. Furthermore, we also give a numeric solution using a splitstep algorithm, and also present two physical applications of the sinegordon equation. We propose a method to deal with the general sine gordon equation. Lyngby, denmark in this exercise we are considering a horizontal along z, periodic distance a, linear. Quantum simulation of klein gordon equation and observation of. The sine gordon equation is a nonlinear hyperbolic partial differential equation involving the dalembert operator and the sine of the unknown function. We start with a basic equation called gordons growth model, p d r g, where p is price, d is dividend, r is the required rate of return, and g is the growth of dividends over time. It is described by an equation of motion which reduces to the ordinary sine gordon equation when the noncommutation. Stationary baseband solutions of the equation come about as a balance between nonlinearity and dispersion, and thus represent solitary wave solutions to the system.
Numerical study of the nonlinear kleingordon equation. Theory of the earth california institute of technology. In this work, we use a reproducing kernel method for investigating the sinegordon equation with initial and boundary conditions. Compared with previous solutions, our solutions are more general than some of the previous. Let us look for solutions of the sinegordon equation. It was originally considered in the nineteenth century in the course of study of surfaces of constant negative curvature. C, we explicitly solve the marchenko equations by separation of variables. In this section, we give the basic theory of the sine gordon equation and the variety of its travelingwave solutions, as spatiotemporal models of nonlinear excitations in complex physical systems. In practice, however, most column struts suffer plastic knockdown and the experimentally obtained buckling loads are much less than the euler predictions. The approximate analytical solution of the equation is calculated in the form of a series with easily computable components.
By rearranging the terms in the equation, the gordon growth model can be used to relate the pd ratio to dividend growth and the discount rate. In the quasiclassical quantization of the field, a fundamental role is played by the above formulas for and. It is a generalized form of the kleingordon equation u tt. Is the klein gordon equation the same in all reference frames. The kleingordon equation is that of the motion of a quantum scalar or pseudoscalar. Fun with the gordon growth model calculating investor. It is known that, if f is almost periodic and not too large, the pendulum equation has almost periodic solutions. Lorentz transformations the free particle kleingordon equation. These results indicate that the reproducing kernel method is very effective. A note on the three dimensional sinegordon equation. A qualitative study of the damped dung equation and applications. The gordon equation states that the longterm expected real inflation adjusted return from the market should approximate the inflationadjusted compound yearly growth rate in dividends plus the current dividend yield. Chapter 5 sinegordon equation the sinegordon equation is a nonlinear hyperbolic partialdifferential equation involving the dalembert operator and the sine of the unknown function.
A qualitative study of the damped dung equation and. Vahidi department of physics, faculty of science urmia university, urmia, p. Kaya 7 has implemented the decomposition method for solving the sinegordon equation by using a number of initial values in the form of. Numerical solution to the sinegordon equation defined on. Clearly, the fact that c 1 is a consequence of the use of scaled coordinates. One and two soliton solutions for the sinhgordon equation in. The acquired results are compared with the exact solutions and results obtained by different methods. Sinegordon equation in this talk, by applyingthe ist and the marchenko method, we get explicit solutions to the sine gordon equation.
For a fixed growth rate, g, we can relate pd to the discount rate r. The sinegordon equation is a nonlinear hyperbolic partial differential equation involving the dalembert operator and the sine of the unknown function. Pdf the sinegordon equation as a model classical field. Notes on the sine gordon equation david gablinger january 31, 2007 abstract in this seminar, we will introduce the sine gordon equation, and solve it using a baecklund transfomation. Based on nonlinear spectral analysis, exact nonreflecting boundary conditions are derived at two artificially introduced boundary points.
Method for solving the sinegordon equation university. Generalized solution of sinegordon equation 7 2016 no. Bohmian mechanics of kleingordon equation via quantum metric. The representation on solutions of the sinegordon and klein. The first terms on their righthand sides correspond to particles of mass and. This is no longer a soliton equation, but it has many similar properties, as it is related to the sine gordon equation by the analytic continuation or wick rotation y it. The graph below shows how pd relates to r for fixed growth rate of 5%. When e is negative, the reaction is not spontaneous.
A new approach for onedimensional sinegordon equation. In this article, we have checked the representation on solutions of sinegordon and kleingordon equations by laplace transform. This paper gives three new solutions to solve the 2d sinegordon equation. On changing the sign of the second term in equation 1, one gets the following partial di erential equation which has solutions of type a if ux. For other exact solutions of the sinegordon equation, see the nonlinear kleingordon equation with fw bsinw. The method is based on collocation of modified cubic bsplines over finite elements, so we have continuity of the dependent variable and its first two derivatives throughout the solution range. Gordon of the university of toronto, who originally published it along with eli shapiro in 1956 and made reference to it in 1959. The initial value problem for the sine gordon equation is solved by the inversescattering method. The equation, as well as several solution techniques, were known in the nineteenth century in the course of study of various problems of differential geometry. Notes on the sine gordon equation david gablinger january 31, 2007 abstract in this seminar, we will introduce the sinegordon equation, and solve it using a baecklund transfomation. The sinegordon equation is integrated by the inverse scattering method.
The basic aim of this paper is to introduce and describe an efficient numerical scheme based on spectral approach coupled with chebyshev wavelets for the approximate solutions of kleingordon and sinegordon equations. Modified cubic bspline collocation method is discussed for the numerical solution of onedimensional nonlinear sinegordon equation. The first terms on their righthand sides correspond to particles of mass and to particles of the ground field, respectively cf. All the results are calculated by using the symbolic calculus software matlab 20a and mathematica. Example 1 25 we consider the nonlinear klein gordon equation with, and in the interval with the initial conditions. The same is true for the three dimensional sinegordon equation. Equations 1 and 2 are actually the solutions to these pdes. The equation most widely used is called the gordon growth model ggm. In other words, it is used to value stocks based on the net present value of the future dividends. So, if the current dividend yield is 2% the gordon equation would predict a 3. Classically we have the hamiltonian for a free particle.
A ear y later, b lam and witz, ablo kaup, ell, new segur produced erse v in scattering metho ds to e solv the equation, reducing. The sinegordon equation is the eulerlagrange equation for this lagrangian. There is a growing interest in the study of the sinhgordon equation, the double sinhgordon. Then the sinegordon equation will take the form c 0 2. The representation on solutions of the sinegordon and. We propose a method to deal with the general sinegordon equation. Theres a very elegant proof of this equation, which you can read about here. Method for solving the sinegordon equation university of. Multisoliton solutions and quasiperiodic solutions of nonlinear equations of sinegordon type etsuro date received june 11, 1980 in this paper we are concerned mainly with the sinegordon equation 0. This paper gives three new solutions to solve the 2d sine gordon equation.
The nernst equation is derived from the emf and the gibbs energy under nonstandard conditions. New travelling wave solutions for sinegordon equation. It shows interesting quantum relativistic phenomena. Furthermore, we also give a numeric solution using a splitstep algorithm, and also present two physical applications of the sine gordon equation. The dividend discount model ddm is a method of valuing a companys stock price based on the theory that its stock is worth the sum of all of its future dividend payments, discounted back to their present value.
May 18, 2011 the basic idea behind dcf analysis is as follows. Pdf numerical solution of kleingordon and sinegordon. The main characteristic is that, it converts the given problem into a system of algebraic equations that can be solved easily with any of the usual methods. One and two soliton solutions for the sinhgordon equation. Numerical solution of kleinsinegordon equations by. Of particular interest is the domain wall collision to 2d sinegordon equation which to the authors knowledge have not been presented in the literature. Our aim is to extend this result to the sinegordon equation. Pdf exact solutions of coupled sinegordon equations. Numerical solution of nonlinear sine gordon equation with local rbfbased nite di erence collocation method y. Predictions of buckling loads by the euler formula is only reasonable for very long and slender struts that have very small geometrical imperfections. A crucial tool in the proofs is a recent maximum principle for. Solutions of the kleingordon equation for the harmonic oscillator potential plus nad potential h.
In the present chapter, we consider two prototypical klein gordon models. The elliptic sinh gordon equation may be defined in a similar way. Di erential equations and modeling a di erential equation is simply any equation that involves a function, say yx and any of its derivatives. Numerical solution of nonlinear sinegordon equation with. Numerical solution of nonlinear sinegordon equation with local rbfbased nite di erence collocation method y. Numerical simulation of the solution to the sinegordon equation on the whole real axis is considered in this paper. The sinhgordon equation appears in integrable quantum field theory, kink dynamics, fluid dynamics, and in many other scientific applications. The above equation uses the prime notation 0 to denote the derivative, which has the bene t of resulting in compact equations. The equation leads to the development of dirac equation and hence quantum field theory. The initial value problem for the sinegordon equation is solved by the inversescattering method.
Actually, there exist even deeper analogies between 1. Numerical experiments are studied to show the efficiency of the technique. In this section, we give the basic theory of the sinegordon equation and the variety of its travelingwave solutions, as spatiotemporal models of nonlinear excitations in complex physical systems. E ooxidation when o e o is positive, the reaction is spontaneous. The partial molal free energy or chemical potential per mole of species i is f, where a, is the activity of a chemical species, and fp is the free energy in a standard state. Furthermore, one of the distinguished features of the ch equation is that it possesses certain nonsmooth travelingwave solutions called peakons. It should be noted that this is an expectation, and not at all a guarantee. Several new exact travelling wave solutions with the form of jacobiamplitude function are derived for the general sine gordon equation by using some reasonable transformation. The coupled sinegordon equation, which can be used to describe the propagation of an optical.
Numerical solution of kleinsinegordon equations by spectral. The main purpose of this work is to extend other studies and to emphasize the power and the efficiency of the tanh method. Of particular interest is the domain wall collision to 2d sine gordon equation which to the authors knowledge have not been presented in the literature. To give the clear overview of this method we consider three examples of klein gordon equation and sine gordon equation. In section 5 we also explore the relationship between the lyapunov equations and the sylvester equation and show how their solutions are related to each other in a simple but interesting way. Numerical solution of sinegordon equation by reduced. Introduction to dispersive waves, dispersion relations, uniform kleingordon equation, linear superposition and the fourier transform, the stationaryphase method for linear dispersive waves 20 extra lecture pdf. The gordon equation can it predict future market returns. Abstract reduced differential transform method rdtm, which does not need small parameter in the equation is implemented for solving the sinegordon equation.
It was originally introduced by edmond bour in the course of study of surfaces of constant negative curvature as the gausscodazzi equation for surfaces of curvature. G, is also related to spontaneity of a reaction, therefore. Rankine gordon equation predictions of buckling loads by the euler formula is only reasonable for very long and slender struts that have very small geometrical imperfections. Numerical solution of kleingordon and sinegordon equations using the numerical method of gridless lines. Lyngby, denmark in this exercise we are considering a horizontal along. Several new exact travelling wave solutions with the form of jacobiamplitude function are derived for the general sinegordon equation by using some reasonable transformation. The kleingordon equation is a relativistic wave equation, related to the schrodinger equation. Sine gordon equation in this talk, by applyingthe ist and the marchenko method, we get explicit solutions to the sine gordon equation. The kleingordon equation for a free particle has a simple planewave solution. Sinegordon equation neqwiki, the nonlinear equations. Solutions of the kleingordon equation for the harmonic.
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