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The Sine-Gordon Model and Its Applications: From Pendula and

Ekvivalensen mellan sine-Gordon modellen och massiva Thirring model har härletts, där ekvivalensen syftar på att teorierna, trots att beteendet hos fermionfält och bosonfält skiljer sig, beskriver exakt samma fysik. Den massiva Schwinger modellens ekvivalens med en motsvarande bosonfält teori har även härletts. 2019-03-04 · The final threshold $\beta=\sqrt{2}$ corresponds to the Kosterlitz-Thouless (KT) phase transition of the $\log$-gas. In this paper, we present a novel probabilistic approach to renormalization of the two-dimensional boundary (or 1-dimensional) Sine-Gordon model up to the KT threshold $\beta=\sqrt{2}$. Sine-Gordon方程是十九世纪发现的一种偏微分方程，由于Sine-Gordon方程有多种[[孤立子]]解而倍受瞩目。 L'equazione di sine-Gordon (o equazione di seno-Gordon) è un'equazione differenziale alle derivate parziali iperbolica non lineare in 1 + 1 dimensioni, che coinvolge l'operatore di d'Alembert e il seno della funzione incognita. È stata originariamente introdotta da Edmond Bour (nel 1862) nel corso dello studio delle superfici a curvatura negativa costante, come l'equazione di Gauss 2012-01-01 · The well-known sine–Gordon and complex sine–Gordon equations are actively used in the study of various physical models and processes such as self-induced transparency and coherent optical pulse propagation, relativistic vortices in a superfluid, nonlinear sigma models, the motion of rigid pendulum, dislocations in crystals and so on (see, for instance, references in , , , , , , ).

Sine gordon

The sine-Gordon equation is a traditional wave equation with a sine function term. This equation and its modifications are widely applied in physics and engineering. It used to describe the spread of crystal defects, the propagation of waves, the extension of biological membranes, relativistic field theory, 1 – 3 it can reduce to the Klein The Sine-Gordon expansion method is implemented to construct exact solutions some conformable time fractional equations in Regularized Long Wave (RLW)-class. Compatible wave transform reduces the governing equation to classical ordinary differential equation. 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 high-energy physics models.

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Gordon Allport, fadern till personlighetspsykologin, dog den 9 oktober 1967. 2020-04-14 · The sine-Gordon equation is a traditional wave equation with a sine function term. This equation and its modifications are widely applied in physics and engineering.

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kink-kink (odd parity Sine-Gordon equation Last updated January 17, 2021.

∂t2. = a. [42] has catalogued many exact solutions to the sine-Gordon equation in terms of elliptic functions. Some of these solutions, including the one-soliton solution, May 24, 2019 In this model, the discrete analog of the sine-Gordon equation is derived. Instead of taking the continuous limit, the space step between The sine-Gordon model is a ubiquitous model of Mathematical Physics with a wide range of applications extending from coupled torsion pendula and.
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It de-scribes simplest possible interaction Hamiltonian between chiral edge modes of each layer. Unlike well-known Sine-Gordon theory which shows Kosterlitz-Thouless type ow, chiral version of Sine-Gordon theory behaves di erently under RG. 2020-01-01 The Solution to the 3D sine-Gordon equation The sine-Gordon expansion method; which is a transformation of the sine-Gordon equation has been applied to the potential-YTSF equation of dimension (3+1) and the reaction-diffusion equation. We obtain new solitons of this equation in the form hyperbolic, complex and trigonometric function by … Sine{Gordon equation can b e ed solv exactly y b analytical hniques. tec This as w an area of vigorous h researc in the early 1970s, with rst solution pro duced through direct metho ds y b Hirota in 1972.
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We may consider it as the square root of the Planck constant: = p ~. Indeed, let u(x) = ’(x). Then the action The sine-Gordon model has universality and appears in various ﬁelds of physics[9–12].