Chapter 5 sinegordon equation the sinegordon equation is a nonlinear hyperbolic partialdifferential equation involving the dalembert operator and the sine of the unknown function. Gordon growth model guide, formula, examples and more. For as we shall see later in this book, it is certainly not that nature fundamentally follows these abstractions. The solution is reduced to solving a set of linear hyperbolic partial differential equations. A numerical algorithm of solving the forced sinegordon. 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. Ruffinni from mactutor history of mathematics archive. Skip to main content this banner text can have markup. Or if youre more of a peopleperson, you can read about the career of myron j. Vahidi department of physics, faculty of science urmia university, urmia, p. Existence of travelling waves in discrete sinegordon. Numerical simulation of the solution to the sinegordon equation on the whole real axis is considered in this paper. In addition, the equations of the theory permit topological nontrivial solutions called solitons. In the present chapter, we consider two prototypical klein gordon models.
If you write fiction, susan may warrens the story equation is a book you need to buy. Including the lineages of his sons, lorenzo dow gordon and bennett nathanial gordon. Albert einsteins famous equation emc 2 for the first time connected the mass of an object with its energy and. Kleingordon equation in electromagnetic environment. We will identify the assumptions required in the model. Historically, the kleingordon equation was the first relativistic equation in quantum mechanics for the wave function. The plane waves 10 are basic solutions and the field 9 is constructed by. The sine gordon model is a toy model that helps to understand fundamental notions like duality in a simplified setup. 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. The riemann function method is used to find a solution of a linear pde. 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 threedimensional solutions depend on arbitrary functions f. We focus, in particular, on two of their prototypical solutions, namely the kinklike heteroclinic connections and the timeperiodic, exponentially localized in space breather waveforms.
Gordon college bookstore follett college campus store. The equations for stationary configurations of the fk model reduce to those of the standard map or chirikovtaylor map of stochastic theory. 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. Why is the klein gordon equation of second order in time. Deloreans claims relied on gordon novels investigation and resulting evidence.
A comparison of the rankine gordon and euler equation, for geometrically perfect struts, is given below. The sinegordon model and its applications from pendula. 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. Delorean claimed there was a conspiracy between britains conservative party and u. Applications and connections the sine gordon equation is used in fields as wide as. Solutions of the klein gordon equation for the harmonic oscillator potential plus nad potential h. 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. Complete discrimination system for polynomial and direct integral method were discussed systematically.
Sinegordon equation neqwiki, the nonlinear equations. 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. New numerical results are reported regarding the solutions of a singularly perturbed sine gordon equation, modeling magnetic flux quanta fluxons in. 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. 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. The purpose of this book is to present a summary of recent developments in this field, incorporating both introductory. In the continuumlimit approximation the fk model reduces to the exactly integrable sinegordon equation or sg equation which allows for soliton solutions. The cauchy problem for the sine gordon equation can be solved using the inverse scattering transform. A partial differential equation which appears in differential geometry and relativistic field theory. It was originally considered in the nineteenth century in the course of study of surfaces of constant negative curvature. Due to the kleingordon equation s enormous popularity, the sge was named so as a wordplay. Solutions of the threedimensional sinegordon equation. 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. All structured data from the file and property namespaces is available under the creative commons cc0 license.
Asymptotic behaviour of solitonantisoliton solution for the sine gordon equation. Miller, department of mathematics, university of michigan, east hall, 530 church st. The books homepage helps you explore earths biggest bookstore without ever leaving the comfort of your couch. Ndsolvevalueeqns, expr, x, xmin, xmax, y, ymin, ymax solves the partial differential equations eqns over a rectangular region. History of the gordon family as descended from james gordon. The full solution of the equation is a rather complicated problem, so we limit ourselves to particular solutions, one of which is the soliton. It simply provides a statistical calculation of the peak load for a sdof system. I mean, normally you would expect that as soon as you fix the initial wavefuncti.
Gordon northcott and the wineville chicken coop murders. 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. The sine gordon equation is a nonlinear hyperbolic partial differential equation involving the dalembert operator and the sine of the unknown function. Sufficient conditions on the initial data for which each problem may be solved by the inverse scattering transform are given. Solitary wave interactions in dispersive equations using.
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. In other words, it is used to value stocks based on the net present value of the future dividends. It is secondorder in space and time and manifestly lorentzcovariant. For this reason the fk model is also known as the discrete sinegordon or periodic kleingordon equation. The equivalence of the methods for solving both the goursat problem and the cauchy problem for the sine gordon equation is discussed. Unperturbed sinegordon equation has exact solution. Files are available under licenses specified on their description page. I was wondering if there is any way to interpret the fact that the klein gordon equation is a 2nd order pde in time.
The kleingordon equation kleinfockgordon equation or sometimes kleingordon fock equation is a relativistic wave equation, related to the schrodinger equation. Furthermore, one of the distinguished features of the ch equation is that it possesses certain nonsmooth travelingwave solutions called peakons. Based on nonlinear spectral analysis, exact nonreflecting boundary conditions are derived at two artificially introduced boundary points. To illuminate the vital relationship between history and geographical conditions, w. Nonlinear partial differential equations for scientists. Asymptotic behaviour of solitonantisoliton solution for. 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. Stability theory for the damped sinegordon equation. 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. Kleingordon equation article about kleingordon equation. Their discussion includes experimental observations of solitons, the inverse scattering. The origins of the clan gordon and their place in history scottish clan minibook on. 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.
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. Equations 1 and 2 are actually the solutions to these pdes. The kleingordon equation is a relativistic wave equation, related to the schrodinger equation. In 1823, norwegian mathematician niels henrik abel ended the discussion of the question of our interest. Soliton is a kink which changes the josephson phase from 0 to 2. Introduction to relativistic quantum mechanics 249 1.
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. 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. 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. Its name is a wordplay on its similar form to the kleingordon. It is a quantized version of the relativistic energymomentum relation. Investors can then compare companies against other industries using this simplified model. 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.
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. The purpose of this book is to present a summary of recent developments in this. The origins of the clan gordon and their place in history scottish. Direct integral method, complete discrimination system for. Bob gardners the bicentennial of evariste galois brief. However, our sine gordon problem is a twodimensional one space one time problem. The sinegordon model is a ubiquitous model of mathematical physics with a wide. In this present work we are dealing with two partial differential equation named as kleingordon and sinegordon equations. These primordial postulates are the only building blocks of a model that explains the inevitable course of events that created our universe. Siam journal on applied mathematics siam society for. 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. Nonlinear evolution equations and hyperelliptic covers of.
We study the general properties of spectral curves associated to doublyperiodic solutions of kortewegdevries, sine gordon, nonlinear schr\\odinger and 1d. The klein gordon equation kleinfock gordon equation or sometimes klein gordon fock equation is a relativistic wave equation, related to the schrodinger equation. 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. Let us look for solutions of the sinegordon equation. Localization of the sine gordon equation solutions article in communications in nonlinear science and numerical simulation 39. The gordon equation can it predict future market returns. 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. Gordon s theory of everything starts with only two postulates.
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. 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. 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. An analytical study is conducted of the structure, stability, and bifurcation of the spatially dependent timeperiodic solutions of the dampeddriven sine gordon equation. Klein gordon equation article about klein gordon equation. Experimental results for the sinegordon equation in arrays of coupled torsion pendula. 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. The goursat and cauchy problems for the sinegordon.
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. Gordon college bookstore in wenham, ma for directions, information, textbook rentals and cheap college textbooks. Furthermore, we also give a numeric solution using a splitstep algorithm, and also present two physical applications of the sine gordon equation. 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. Solutions of the kleingordon equation for the harmonic. Its name is a wordplay on its similar form to the klein gordon. History of the gordon family as descended from james gordon of new york. Along the way we see menos paradox and how pythagoras had nothing to. 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.
How to obtain the accurate solution of kleingordon equation. The sinegordon equation is a nonlinear partial differential equation. Computation and stability of fluxons in a singularly. It may be used to great effect as a course textbook, research reference, or selfstudy guide. Localization of the sine gordon equation solutions. Two limits of the discrete variants of these models are. We prove existence results for travelling waves in discrete, damped, dcdriven sine gordon equations with periodic boundary conditions. Here youll find current best sellers in books, new releases in books, deals in books, kindle ebooks, audible audiobooks, and so much more. Buckingham, department of mathematical sciences, university of cincinnati, po box 210025, cincinnati, ohio 45221 and peter d. Search the history of over 424 billion web pages on the internet. 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. The sinegordon model and its applications springerlink.
In particularly, we pointed out some mistaken viewpoints. History media compliance careers affiliate program. Discover delightful childrens books with prime book box, a subscription that. This page was last edited on 18 august 2017, at 18. He successfully proved that there is no algebraic equation to give the solutions to a general fifth degree polynomial equation. In this lesson, we will learn how stocks are valued using the gordon growth model. Ca history of science special relativity formalism. 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. At the very least it should be consistent with the theory of spe cial relativity that had revolutionized classical physics. Klein gordon equation the quest for a mathematical theory of quantum mechanics began with great am bition. 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. Many basic features of such solitons can be studied in the sine gordon. The sinegordon model and its applications from pendula and.
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