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There it is the Mainardi-Codazzi equation, i.e. the integrability condition, of a pseudospherical surface given in (arc-length The sine-Gordon model as the theory of a massless scalar field in one space and one time dimension with interaction Lagrangian density proportional to cos/9tf is generalized for scalar superfield ; id it is shown that the solution of the supercovariant sine-Gordon equation 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 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]).

Its hamiltonian is. H = ∫. I dx. (. 1.

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.

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Key words and phrases. Elliptic sine-Gordon equation, variational methods, numerical computation.

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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.

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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 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]). 2011-10-04 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 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.

Lecture 1: sine-Gordon equation and solutions • Equivalent circuit • Derivation of sine-Gordon equation • The most important solutions plasma waves a soliton! chain of solitons resistive state breather and friends • Mechanical analog: the chain of pendula • Penetration of magnetic ﬁeld Introduction to the ﬂuxon dynamics in LJJ Nr. 2 Equation (6.56) is identical to the sine–Gordon equation used to describe commensurate-incommensurate transitions in solids, for which structural configurations correspond to minima of the effective potential V [4].For the purposes of the current discussion, we will neglect the q–dependence of δ and assume that it is fixed.We note, however, that it is possible for δ to become negative as 1996-02-01 The symmetric space sine-Gordon models arise by conformal reduction of ordinary 2-dim $\sigma$-models, and they are integrable exhibiting a black-hole type 2021-03-16 Lagrangian. In Section 3, sine-Gordon kinks with a modiﬁed mass term and their non-Abelian. U(N) generalization are discussed.
Active 1 year, 3 months ago. Viewed 61 times 4. 5 $\begingroup$ I recently came across a paper of Witten that talks about the S-matrix of the supersymmetric non-linear sigma model. In the Notes on The Sine Gordon Equation David Gablinger January 31, 2007 Abstract In this seminar, we will introduce the Sine-Gordon equation, and solve it using a Baecklund transfomation.