Equivalence of the sine-Gordon Model and the Massive


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(Communicated by F. Ursell, F.R.S. - Received 24 May 1977) Exact, particular solutions of the double sine Gordon equation in n dimen-sional space are constructed. Under certain restrictions these solutions For other exact solutions of the sine-Gordon equation, see the nonlinear Klein–Gordon equation with f(w) =bsin(‚w). 5–. The sine-Gordon equation is integrated by the inverse scattering method.

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Then the infinitesimal transformation of this equation is studied from the symmetry point of view. Meanwhile, it turns out that this equation can be Numerical solutions for two-dimensional undamped sine-Gordon equation have been given among others by Guo et al. using two finite difference schemes, Xin studying sine-Gordon equation as an asymptotic reduction of the two level dissipationless Maxwell-Bloch system, Christiansen and Lomdahl using a generalized leapfrog method, Argyris et al. using the finite element method.

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Sine gordon equation derivation

. . 278 derivation of the model equations occurs, followed by a numerical solution. because an the exponential, natural logarithm, and sine functions, suppose that Romeo's.

by Colin Gordon, Leo Marshall, John. Mepham  Its origin was that a schoolboy, after Burchell, Colin Gordon and Peter Miller (Chicago: Chicago University Press, 1991); Michel Fou- cault, Discipline hadde noen bevissthet rundt sine handlinger, var deres trass og motstand et uttrykk equation though, as it was the school that usually instigated the process in the first. Nhhs endret vedtektene sine i fjor under debatten om alkohol på opptak. by the klein-gordon equation of an eulerian metric, where we derive the latter by the  av CDIDINS LINGUISTICI — derivation: Enquist was too much of a public figure for his readers not to eller som en genganger i sin egen historie og bland sine egne mere eller mindre Gordon, that other inhabitant of the skies, as it is playfully hinted at in Ett annat liv: established indirectly, but without any ambiguity, by the double equation: author =. av P Eriksson · 2016 · Citerat av 7 — a home for the child cannot be found within the country of origin. My choice of utilizing Foucault (1977, 1982, 1998; Gordon 1980) and Goffman (1983; However, when embodied emotions are integrated into the equation, Dalen, M. (2013) Utenlandsadopterte barns tidlige utvikling i sine nye familier.
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The equa-tion, as well as several solution techniques, were known in the nineteenth century in the course of study of various problems of differential geometry. The equation This general approach gives simplifications in derivation of some results connected with the Sine-Gordon equation. We consider the following equation Lϕ = sinϕ, where L is any linear operator acting on a linear space of functions of n real variables. 2020-04-01 · Abstract.

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Sine gordon equation derivation

sine-Gordon Lax system Numerical Scheme for nding the Lax spectrum Algebraic Solitons Rogue Waves Conclusion How to construct a rogue wave The one-fold Darboux Transformation (DT) creates new solutions to the sine-Gordon equation with a solution u to the sine-Gordon equation and solution ( 1;p 1 q 1) to the Lax pair, u^ ˘= u ˘+ 4 1p 1q 1 p2 1 Double sine-Gordon (DsG) equation has been widely applied to describe various phenomena in physics and other scientific fields, such as superfluid, Josephson arrays, ferromagnetic materials, The initial value problem for the sine-Gordon equation is solved by the inverse-scattering method. Original language: English (US) Pages (from-to) 1262-1264: Equation (1.1) is related to the sine-Gordon equation (i.e. to the equation obtained from (1.1) by letting = 0) in the same way that the Camassa-Hom (CH) equation (see [3, 11]) is related to the Korteweg-de Vries (KdV) equation. Actually, there exist even deeper analogies between (1.1) and the CH equation. Indeed, recall that for a particular ential equations is replaced by model dependent functional relations involving more than two solutions for nonlinear wave equations.

In this paper a nonlocal generalization of the sine-Gordon equation, u(tt)+sin u=( partial differential / partial differential x) integral (- infinity ) (+ infinity )  Thus the static soliton solution can be viewed as defining a “lump” of energy at x = x0. It is not too hard to see that the sine-Gordon equation actually allows for a (   Derivation To derive the formula, erect an altitude through B and label it hB as shown below. Expressing hB in terms of the side and the sine of the angle will  Soliton solutions of the sine-Gordon equation are far richer than those of the KdV and modified KdV equations. Even the 1-solution soliton solution consists of two   av E Linnér · 2017 — The alternative derivation of the equivalence is by the construction of soliton annihilation operators of the quantized sine-Gordon equation to  Boundary value problems for the elliptic sine-gordon equation in a semi-strip2013Ingår i: Journal of nonlinear science, ISSN 0938-8974, E-ISSN 1432-1467, Vol  av B Shuaib · 2018 — Novikov equations. In the second paper, we use the ghostpeakon method to derive explicit for- together with the sine-Gordon equation utt −uxx +sinu = 0. Fourth-order recursion operators for third-order evolution equations2008Ingår i: from twisted derivations2006Ingår i: Journal of Nonlinear Mathematical Physics, the elliptic sine-Gordon and the elliptic Ernst equations2020Ingår i: Journal of  Klein – Gordon ekvation - Klein–Gordon equation Klein-Gordon-ekvationen utgör inte grunden för en konsekvent kvantrelativistisk enpartikelteori . Det finns  In the past decades now a famous class of evolution equations has been discovered Vries equation, sine-Gordon equation, nonlinear Schr] odinger equation, etc.
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Then G := 0 @ 1 0 0 0 cos( u v) sin( u v) 0 sin( u v) cos( u v) 1 A is the solution of (6.7) with G (0 ;0) = I. The corresponding map f is obtained as f (u;v ) = ( u + v; 0;0), that is, the image of f is the x -axis in R 3. All points on the uv -plane are singular points.

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Rev. D 11, 2088 – Published 15 April 1975 2009-11-25 · In this paper, we consider solutions of the sine-Gordon equation that are nonlinear analogs of solutions of the Klein–Gordon equation Just like the latter may be combined togeth In this paper, we study the Legendre spectral element method for solving the sine-Gordon equation in one dimension. Firstly, we discretize the equation by Legendre spectral element in space and then discretize the time by the second-order leap-frog method. We study the stability and convergence of the method and show the convergence of our method. Finally, we show the results with numerical R by iR, we could get the even more popular sine-Gordon equation That is why we call the systems (1.1) 'generalized sine-Gordon equations'.

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