14 Jun 1977 interaction Lagrangian density proportional to cos/9tf is generalized it is shown that the solution of the supercovariant sine-Gordon equation.

The designation “sine-Gordon” is also used for various equations that generalize [1] or bear resemblance to it. These include the so-called homogeneous and symmetric space sine-Gordon models, discrete and supersymmetric versions, and generalizations to higher-dimensional spacetimes (i.e., in [1] the spatial derivative is replaced by the Laplace operator in several variables).

Expert Answer . Previous question Next question Transcribed Image Text from this Question. L = (03 – 02) + cosø Topologically stable non-Abelian sine-Gordon solitons have been found recently in the U(N) chiral Lagrangian and a U(N) gauge theory with two N by N complex scalar fields coupled to each other. We construct the effective theory on a non-Abelian sine-Gordon soliton that is a nonlinear sigma model with the target space R×CPN-1. The sine-Gordon model has a universality and appears in various fields of physics [1-4].

References Steuerwald, R., Uber enneper’sche Fl¨ achen und B¨ ¨acklund’sche Transformation, Abh. Bayer. Akad. Wiss. (Muench.), Vol. 40, pp Sine-Gordon BPS fields in (1+1) dimensions Wojtek J Zakrzewski (Durham Univ)a abased on work carried out with P.Klimas (Florianopolis), L.A. Ferreira (Sao Carlos) and A. Wereszczynski (Krakow) Introduction General case of 2 elds in (1+1) dimensions Two Fields BPS conditions for 2 elds Numerical support BPS conditions for two Sine Gordon elds.

Wiss. (Muench.), Vol. 40, pp The name "sine-Gordon equation" is a pun on the well-known Klein–Gordon equation in physics: \varphi_{tt}- \varphi_{xx} + \varphi\ = 0.\, The sine-Gordon equation is the Euler–Lagrange equation of the field whose Lagrangian density is given by \mathcal{L}_\text{SG}(\varphi) = \frac{1}{2}(\varphi_t^2 - \varphi_x^2) - 1 + \cos\varphi.

Lagrangian formalism to study the eﬀect of damping and external forces in the nonlinear Klein-Gordon systems, and in particular we use as examples sine-Gordon (sG) and φ4 (this method can be extended to other nonlinear Klein-Gordon equations such as, the double sine-Gordon (DsG) [3] or the asymmetric double sine-Gordon (ADSG) [6]).

Wiss. (Muench.), Vol. 40, pp The name "sine-Gordon equation" is a pun on the well-known Klein–Gordon equation in physics: \varphi_{tt}- \varphi_{xx} + \varphi\ = 0.\, The sine-Gordon equation is the Euler–Lagrange equation of the field whose Lagrangian density is given by \mathcal{L}_\text{SG}(\varphi) = \frac{1}{2}(\varphi_t^2 - \varphi_x^2) - 1 + \cos\varphi. Chiral sine-Gordon model The sine-Gordon model is given by[11, 15] L = 1 2t (∂µϕ) 2 + α t cosϕ, (1) where ϕ is a real scalar ﬁeld.

The sine-Gordon model has a universality and appears in various fields of physics [1-4]. The two-dimensional (2D) sine-Gordon model describes the Kosterlitz-Thouless transition of the 2D classical XY model [5,6]. The 2D sine-Gordon model is mapped to the …

The straight red line indicates Fast Lagrangian Analysis of Continua, FLAC är ett finit differensprogram för simulering av stora töjningar i Griffiths, D.V. Gordon, A. Fenton, M. 2004. Probabilistic Slope (Lagrange's Theorem) If a group G of order N has a subgroup H of order. n then the index of If we consider only small rotations, we can expand the sine and cosine terms to first order.

We provide a Lagrangian formulation of these systems by considering a triplet of Lie groups F ⊃ G ⊃ H. This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia.
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2 Jun 2016 The classical Sine-Gordon Model is a 2d-field theory and can be characterized as a hamiltonian system. Its hamiltonian is. H = ∫. I dx. (. 1. 2.

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Then, that also improves the analogy with the Klein-Gordon Lagrangian density, as there is no longer the need to subtract 1 from the sine-Gordon Lagrangian density. Just a thought. Evilmathninja 23:06, 22 January 2007 (UTC)

Chiral sine-Gordon model The sine-Gordon model is given by[11, 15] L = 1 2t (∂µϕ) 2 + α t cosϕ, (1) where ϕ is a real scalar ﬁeld. This Lagrangian is written as, by deﬁning g = eiϕ ∈ U(1), L = 1 2t ∂µg∂ µg−1 + α 2t quantitative conclusions. The Lagrangian under consideration is L(*) - ^{|ф2-с 0 2ф х 2-« р 2(1-совф) ) +ее*ф (1) where the first term represents the sine-Gordon equation for the field ф, and the second one describes the effect of an external field e. The parameters N 0, o 0, u^, e* may be of different micro The Free Klein Gordon Field Theory Jeremy Atkins April 20, 2018 Abstract A single-particle relativistic theory turns out to be inadequate for many situations. Thus, we begin to develop a multi-particle relativistic description of quantum mechanics starting from classical analogies.

This Lagrangian is written as, by deﬁning g = eiϕ ∈ U(1), L = 1 2t ∂ μg∂ μg−1 + α 2t (g +g−1). (2) This is generalized to a general Lie group G: L = 1 2t Tr∂ μg∂μg−1 + α 2t Tr 2 Sine-Gordon model The sine-Gordon model is a theory of a single scalar eld ’(x) in (1+1) dimensions, with the dynamics of the scalar eld being determined by the Lagrangian density L= 1 2 (@ ’)(@ ’) + 0 2 cos( ’) + 0 (2.1) with the position 2-vector x= (x0;x1) and with 0, and 0 de ned as real parameters. As the Lagrangian density is CERN-TH/95-321. ENSLAPP-A-565/95.