# The sine-Gordon model is discussed and analyzed within the framework of the renormalization group theory. A perturbative renormalization group procedure is carried out through a decomposition of the sine-Gordon field in slow and fast modes. An effective slow modes's theory is derived and re-scaled to obtain the model's flow equations.

This paper develops a local Kriging meshless solution to the nonlinear 2 + 1-dimensional sine-Gordon equation. The meshless shape function is constructed by Kriging interpolation method to have Kronecker delta function property for the two-dimensional field function, which leads to convenient implementation of imposing essential boundary conditions.

One can obtain a $\phi^4$ model as an approximation of the sine-Gordon model, expanding the sine term in the equation or cosine term in the Hamiltonian. 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.

This paper develops a local Kriging meshless solution to the nonlinear 2 + 1-dimensional sine-Gordon equation. The meshless shape function is constructed by Kriging interpolation method to have Kronecker delta function property for the two-dimensional field function, which leads to convenient implementation of imposing essential boundary conditions. The sine-Gordon equation is a nonlinear hyperbolic partial differential equation in 1 + 1 dimensions involving the d'Alembert operator and the sine of the unknown function. It was originally introduced by Edmond Bour (1862) in the course of study of surfaces of constant negative curvature as the Gauss–Codazzi equation for surfaces of curvature –1 in 3-space, [1] and rediscovered by Frenkel sine-Gordon model and the massive Thirring model will be derived by identifying that the perturbation expansion terms respectively the commutators of the two theories are identical if certain relations between the quantities of the theories are identi ed. In section 5, The sine-Gordon model has a universality and appears in various ﬁelds of physics [9–12].

## Sine-gordon solitons and black holesIn the talk, the relationship between black holes in Jackiw-Teitelboim(JT) dilaton gravity and solitons in sine-Gordon field

H. in the charge and spin-basis: Free bosons-theory for the charge mode. Sine-Gordon model for the spin mode.

### Bolle og Gordon: Pappaen med de store skoene er et vakkert lite utsnitt i garderobeskapet hans og gråt, så han ikke fikk pakket klærne sine).

Moreover, it is uncovered exact conserved charges associated to two-solitons with a definite parity under space-reflection symmetry, i.e. kink-kink (odd parity Sine-Gordon equation Last updated January 17, 2021. The sine-Gordon equation is a nonlinear hyperbolic partial differential equation in 1 + 1 dimensions involving the d'Alembert operator and the sine of the unknown function.

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Sine, Cosine, Tangent diagram.

Hittade 4 uppsatser innehållade ordet sine-Gordon. 1.

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### Sine-Gordon field theory is used to investigate the phase diagram of a neutral Coulomb gas. A variational mean field free energy is constructed and the corresponding phase diagrams in two (2d) and

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. A ear y later, b Lam and witz, Ablo Kaup, ell, New Segur pro-duced erse v in scattering metho ds to e solv the equation, reducing PDE a able solv The sine-Gordon equations are considered in Euclidean spaces with dimensionality d = 2 and 4.

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### We show that the phase structure of layered two-dimensional (2D) sine-Gordon systems, which interact via an interlayer coupling, depends on the number of

Programplakat Aeroplanes, Deperdussin, Coupe, Gordon-Bennet. 1 picture. Plakat med flagg. Påskrift: Aeroplanes, Deperdussin, Coupe, Gordon-Ben. 1 picture. Alltså kunde Bäcklundtransformationen ses som en transformation mellan två lösningar till sine-Gordon-ekvationen. En Bäcklundtransformation kan också “Norge fikser sine sikkerhetsutfordringer selv?

## Sine-Gordon Equation A partial differential equation which appears in differential geometry and relativistic field theory. Its name is a wordplay on its similar form to the Klein-Gordon equation.

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. 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–Gordon equation 4 , 5 in some special cases.

A partial differential equation which appears in differential geometry and relativistic field theory. Its name is a wordplay on its similar form to the Klein-Gordon equation.The equation, as well as several solution techniques, were known in the 19th century, but the equation grew greatly in importance when it was realized that it led to solutions ("kink" and "antikink The sine-Gordon equation is the Euler–Lagrange equation for this Lagrangian. In the quasi-classical quantization of the field $ u $, a fundamental role is played by the above formulas for $ … Renormalization Group Theory&Sine-Gordon Model. SUMMARY OF THE LECTURES. Lecture 2.