The riemann function method is used to find a solution of a linear pde. We will identify the assumptions required in the model. Gordon northcott and the wineville chicken coop murders. The purpose of this book is to present a summary of recent developments in this. Applications and connections the sine gordon equation is used in fields as wide as. Gordon college bookstore follett college campus store. In most of the early versions the kleingordon equation was connected with the general theory of relativity. A broad class of analytical methods and numerical methods available in the literature are used to handle these problems. Nonlinear evolution equations and hyperelliptic covers of. Klein gordon equation the quest for a mathematical theory of quantum mechanics began with great am bition. Its name is a wordplay on its similar form to the klein gordon.
Vahidi department of physics, faculty of science urmia university, urmia, p. Deloreans claims relied on gordon novels investigation and resulting evidence. Asymptotic behaviour of solitonantisoliton solution for the sine gordon equation. In other words, it is used to value stocks based on the net present value of the future dividends. I could talk in detail about the book s insight, its power to transform your writing, its brilliance, but suffice it to say i predict this will become a classic in the library of how to write bestselling stories. If you write fiction, susan may warrens the story equation is a book you need to buy. An analytical study is conducted of the structure, stability, and bifurcation of the spatially dependent timeperiodic solutions of the dampeddriven sine gordon equation. The sinegordon model and its applications from pendula and.
It was originally considered in the nineteenth century in the course of study of surfaces of constant negative curvature. 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. For struts in this category, a suitable formula is the rankine gordon equation which is a semiempirical formula, and takes into account the crushing strength of the material, its youngs modulus and its slenderness ratio. Discover delightful childrens books with prime book box, a subscription that. Solitary wave interactions in dispersive equations using. A comparison of the rankine gordon and euler equation, for geometrically perfect struts, is given below. Due to the kleingordon equation s enormous popularity, the sge was named so as a wordplay. Then the sinegordon equation will take the form c 0 2. The gordon equation can it predict future market returns. Introduction to relativistic quantum mechanics 249 1.
Along the way we see menos paradox and how pythagoras had nothing to. Nonlinear partial differential equations for scientists. The authors study the cauchy problem for the sine gordon equation in the semiclassical limit with pureimpulse initial data of sufficient strength to generate both highfrequency rotational motion near the peak of the impulse profile and also highfrequency librational motion in the tails. Several numerical solutions to the 1d, 2d, and 3d sinegordon equation are presented and comments are given on the nature of the.
Ndsolvevalueeqns, expr, x, xmin, xmax gives the value of expr with functions determined by a numerical solution to the ordinary differential equations eqns with the independent variable x in the range xmin to xmax. Soliton is a kink which changes the josephson phase from 0 to 2. 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. Gordon growth model guide, formula, examples and more. In addition, the equations of the theory permit topological nontrivial solutions called solitons. The kleingordon equation kleinfockgordon equation or sometimes kleingordon fock equation is a relativistic wave equation, related to the schrodinger equation. 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. 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. Solutions of the kleingordon equation for the harmonic. Experimental results for the sinegordon equation in arrays of coupled torsion pendula. This page was last edited on 18 august 2017, at 18. The sinegordon model is a ubiquitous model of mathematical physics with a wide. The gordon growth model also known as the gordon dividend model or dividend discount model is a stock valuation method that calculates a stocks intrinsic value, regardless of current market conditions. The equations for stationary configurations of the fk model reduce to those of the standard map or chirikovtaylor map of stochastic theory.
Or if youre more of a peopleperson, you can read about the career of myron j. History of the gordon family as descended from james gordon. In his book the investors manifesto, william berstein explains how to use the gordon equation to estimate expected real returns on stocks for stocks on the long run. Large time behavior of solutions to the initial boundary value problems for the damped sine gordon equation are found which guarantee that solutions of the sine gordon equation decay to certain solutions of the corresponding static problem. The equivalence of the methods for solving both the goursat problem and the cauchy problem for the sine gordon equation is discussed. And i suspect that in fact the current predominance of partial differential equations is in many respects a historical accidentand that had computer technology been developed earlier in the history of mathematics, the situation would probably now be very different. Existence of travelling waves in discrete sinegordon. The sinegordon equation is a nonlinear partial differential equation. Investors can then compare companies against other industries using this simplified model. How to obtain the accurate solution of kleingordon equation. We prove existence results for travelling waves in discrete, damped, dcdriven sine gordon equations with periodic boundary conditions.
Kleingordon equation article about kleingordon equation. Localization of the sine gordon equation solutions article in communications in nonlinear science and numerical simulation 39. 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. Computation and stability of fluxons in a singularly. Numerical solution of kleinsinegordon equations by. The numerical method of solving the problem of small perturbations of a stationary traveling solution soliton of wellknown in physics sin gordon equation is presented. This diminutive book explores the history and evolution of the garden, not only as an art form but also as sacred space for a lively partnership between humans and nature. The sine gordon equation in the semiclassical limit. The origins of the clan gordon and their place in history scottish clan minibook on. For as we shall see later in this book, it is certainly not that nature fundamentally follows these abstractions. Exact solutions to the double sinh gordon equation by the tanh method and a variable separated ode method, computers and mathematics with applications, 50 2005 16851696. Miles equation does not give an equivalent static load calculating the g rms value at a resonant peak after a random vibration test and multiplying it by the test article mass does not mean that the test article was subjected to that same, equivalent static load. Let us look for solutions of the sinegordon equation.
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. A numerical algorithm of solving the forced sinegordon. Sinegordon equation neqwiki, the nonlinear equations. Furthermore, we also give a numeric solution using a splitstep algorithm, and also present two physical applications of the sine gordon equation.
A partial differential equation which appears in differential geometry and relativistic field theory. The solution is reduced to solving a set of linear hyperbolic partial differential equations. Numerical simulation of the solution to the sinegordon equation on the whole real axis is considered in this paper. In this lesson, we will learn how stocks are valued using the gordon growth model. It is a quantized version of the relativistic energymomentum relation. All structured data from the file and property namespaces is available under the creative commons cc0 license. Direct integral method, complete discrimination system for. The klein gordon equation kleinfock gordon equation or sometimes klein gordon fock equation is a relativistic wave equation, related to the schrodinger equation. However, our sine gordon problem is a twodimensional one space one time problem. In particularly, we pointed out some mistaken viewpoints. Top american libraries canadian libraries universal library community texts project gutenberg biodiversity heritage library childrens library. Files are available under licenses specified on their description page. It simply provides a statistical calculation of the peak load for a sdof system. Many basic features of such solitons can be studied in the sine gordon.
These primordial postulates are the only building blocks of a model that explains the inevitable course of events that created our universe. We focus, in particular, on two of their prototypical solutions, namely the kinklike heteroclinic connections and the timeperiodic, exponentially localized in space breather waveforms. Chapter 5 sinegordon equation the sinegordon equation is a nonlinear hyperbolic partialdifferential equation involving the dalembert operator and the sine of the unknown function. The sinegordon model and its applications springerlink. Klein gordon equation article about klein gordon equation. In the present chapter, we consider two prototypical klein gordon models. Its name is a wordplay on its similar form to the kleingordon. The great equations is a great book that explains everything you will ever need to know about maths history and the way it has become the way it is today. The full solution of the equation is a rather complicated problem, so we limit ourselves to particular solutions, one of which is the soliton. Asymptotic behaviour of solitonantisoliton solution for. Ca history of science special relativity formalism. In the continuumlimit approximation the fk model reduces to the exactly integrable sinegordon equation or sg equation which allows for soliton solutions. 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. For a singleparticle in a cosine potential, the slightest amount of tunneling between two cosine minima leads to conduction bands, for example, and restores the translational symmetry.
Siam journal on applied mathematics siam society for. Bob gardners the bicentennial of evariste galois brief. At the very least it should be consistent with the theory of spe cial relativity that had revolutionized classical physics. The kleingordon equation is a relativistic wave equation, related to the schrodinger equation. Gordon college bookstore in wenham, ma for directions, information, textbook rentals and cheap college textbooks. Buckingham, department of mathematical sciences, university of cincinnati, po box 210025, cincinnati, ohio 45221 and peter d.
Combining with complete discrimination system for polynomial, direct integral method was developed to become a powerful method and was applied to a lot of nonlinear mathematical. Why is the klein gordon equation of second order in time. We study the general properties of spectral curves associated to doublyperiodic solutions of kortewegdevries, sine gordon, nonlinear schr\\odinger and 1d. 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.
History of the gordon family as descended from james gordon of new york. Delorean claimed there was a conspiracy between britains conservative party and u. In 1928 a string of child abductions culminated in one mothers frantic search for her son, a search that led her to a small farm in wineville and a grisly discovery that shocked a nation. The kleingordon equation in the spacetime representation 9 the quantity q2 is represented by the differential operator dalembert operator from the mass shell condition 6 this results in the kleingordon equation as the basic field equation of the scalar field. History media compliance careers affiliate program. Here youll find current best sellers in books, new releases in books, deals in books, kindle ebooks, audible audiobooks, and so much more. Their discussion includes experimental observations of solitons, the inverse scattering. Furthermore, one of the distinguished features of the ch equation is that it possesses certain nonsmooth travelingwave solutions called peakons. Two limits of the discrete variants of these models are. Unperturbed sinegordon equation has exact solution. Fulfillment by amazon fba is a service we offer sellers that lets them store their products in amazons fulfillment centers, and we directly pack, ship, and provide customer service for these products. In 1823, norwegian mathematician niels henrik abel ended the discussion of the question of our interest. He successfully proved that there is no algebraic equation to give the solutions to a general fifth degree polynomial equation. The origins of the clan gordon and their place in history scottish.
Stability theory for the damped sinegordon equation. Kleingordon equation in electromagnetic environment. The goursat and cauchy problems for the sinegordon. Based on nonlinear spectral analysis, exact nonreflecting boundary conditions are derived at two artificially introduced boundary points. For the origin of the equation, see the constant growth case formula near the bottom of this stock valuation page but think dividends where the page says earnings. Gordon s theory of everything starts with only two postulates. The plane waves 10 are basic solutions and the field 9 is constructed by. Miller, department of mathematics, university of michigan, east hall, 530 church st. It is known that the sine gordon has soliton solutions in the 1d and 2d cases, but such solutions are not known to exist in the 3d case. Solutions of the threedimensional sinegordon equation.
Search the history of over 424 billion web pages on the internet. Localization of the sine gordon equation solutions. Historically, the kleingordon equation was the first relativistic equation in quantum mechanics for the wave function. This is a statement from giamarchis book on quantum physics in 1d. The authors study the cauchy problem for the sinegordon equation in the semiclassical limit with pureimpulse initial data of sufficient strength to generate both highfrequency rotational motion near the peak of the impulse profile and also highfrequency librational motion in the tails. In this present work we are dealing with two partial differential equation named as kleingordon and sinegordon equations. It may be used to great effect as a course textbook, research reference, or selfstudy guide. The sine gordon model is a ubiquitous model of mathematical physics with a wide range of applications extending from coupled torsion pendula and josephson junction arrays to gravitational and highenergy physics models. Albert einsteins famous equation emc 2 for the first time connected the mass of an object with its energy and. Nonlinear partial differential equations for scientists and engineers, third edition,improves onanalready highlycomplete and accessible resource for graduate students and professionals in mathematics, physics, science, and engineering. We obtain exact solutions ux, y, z, t of the threedimensional sinegordon equation in a form that lamb previously proposed for integrating the twodimensional sinegordon equation. Ruffinni from mactutor history of mathematics archive. To illuminate the vital relationship between history and geographical conditions, w.
The purpose of this book is to present a summary of recent developments in this field, incorporating both introductory. New numerical results are reported regarding the solutions of a singularly perturbed sine gordon equation, modeling magnetic flux quanta fluxons in. 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. Chapter 5 sinegordon equation the sine gordon equation is a nonlinear hyperbolic partialdifferential equation involving the dalembert operator and the sine of the unknown function. For this reason the fk model is also known as the discrete sinegordon or periodic kleingordon equation. Complete discrimination system for polynomial and direct integral method were discussed systematically. The cauchy problem for the sine gordon equation can be solved using the inverse scattering transform. Including the lineages of his sons, lorenzo dow gordon and bennett nathanial gordon. Solutions of the klein gordon equation for the harmonic oscillator potential plus nad potential h. I mean, normally you would expect that as soon as you fix the initial wavefuncti. Equations 1 and 2 are actually the solutions to these pdes. It is secondorder in space and time and manifestly lorentzcovariant. Numerical solution to the sinegordon equation defined on. Ndsolvevalueeqns, expr, x, xmin, xmax, y, ymin, ymax solves the partial differential equations eqns over a rectangular region.
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