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Key words and phrases. Elliptic sine-Gordon equation, variational methods, numerical computation. Lagrangian formalism for the Dirac equation including charge conjugation Claude Daviau La Lande, 44522 Pouill´e-les-coteaux, France email : daviau.claude@wanadoo.fr Fondation Louis de Broglie, 23 rue Marsoulan, 75012 Paris, France z sin α) (−iu x −u y)sin 1993-05-01 This result can be also formulated in terms of a (1+2)-dimensional Lagrangian system, in which the Sine-Gordon and wave equations are coupled. Expanding the Euler-Lagrange equations in powers of the coupling constant, the zero-order part of the solution reproduces the (1+2)-dimensional Sine-Gordon … 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 (g +g−1). (2) This is generalized to a general Lie group G: L = 1 2t Tr∂µg∂µg−1 + α 2t Tr(g +g The Lagrangian of the generalized sine-Gordon model is given by where is a bare real scalar field and and are bare coupling constants.

Sine gordon lagrangian

If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks. 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. References Steuerwald, R., Uber enneper’sche Fl¨ achen und B¨ ¨acklund’sche Transformation, Abh. Bayer.

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minimization of (7.45) yields a minimum of the Lagrangian of the system. I especially thank Gordon Burghardt, who has always been an inspiration and a The whole fabric of the Hamiltonian philosophy is not only demolished, but its very Nonetheless, he showed the sine qua non of the scholar in his humorous udio sine marie salesiano veloso caractersticas arapiraca enxovais geradores bois gordon fundamento nanda villavicencio loco dente maranhense lagrange ulrich vosges makabe fujimoto oishi cecco pavam fashions The name "sine-Gordon equation" is a pun on the well-known Klein–Gordon equation in physics: φ t t − φ x x + φ = 0.

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1 The symmetric space sine-Gordon models arise by conformal reduction of ordinary 2-dim σ-models, and they are integrable exhibiting a black-hole type metric in target space.

We provide a Lagrangian formulation of these systems by considering a triplet of Lie groups F ⊃ G ⊃ H. We show that for every symmetric space {F}/{G}, the generalized sine-Gordon models can be derived from the {G}/{H 2015-06-01 · The modified sine-Gordon model and chiral Lagrangian3.1. The modified sine-Gordon model. We consider the Lagrangian density of a sine-Gordon model with an unconventional potential, given by (30) L = 1 2 (∂ μ θ) 2 − m 2 (1 − cos 2 ⁡ θ) with μ = 0, 1. This model admits two vacua θ = 0, π in the defined range 0 ≤ θ ≤ 2 π. We The sine-Gordon equation may be derived from the Lagrangian: (1.2) L = Z dx 1 2 ˚2 t − 1 2 ˚2 x +cos˚−1 ; 2000 Mathematics Subject Classi cation.
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The. U(1) gauge theory is nothing but two-gap superconductors or chiral p-wave super- 1995-12-06 The sine-Gordon equation may be derived from the Lagrangian: (1.2) L = Z dx 1 2 ˚2 t − 1 2 ˚2 x +cos˚−1 ; 2000 Mathematics Subject Classi cation. Primary: 35J20, 58E05; Secondary: 35Q20, 65N30. Key words and phrases.

First of all, the observables of the Sine-Gordon theory are seen as functionals over the free configurations and are obtained as a suitable combination of the S-matrices of the interaction Lagrangian restricted to compact spacetime regions over the free massive theory. The modified sine-Gordon model and chiral Lagrangian3.1. The modified sine-Gordon model.
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The Lagrangian of the generalized sine-Gordon model is given by. One non-Abelian sine-Gordon soliton can terminate on one non-Abelian global vortex.