# Abstract. The paper develops an algebrotopological approach to the problem of effective selection of real finite-zone solutions of the sine-Gordon equation, which uses the socalledγ-representation on the Riemann surface, in which “action” variables can be computed explicitly.

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

2 Jun 2016 The classical Sine-Gordon Model is a 2d-field theory and can be characterized as a In the action we have the quantity L/ standing, so. L = 1. They also showed that a pseudo- spectral method with a high order integrator produced smaller deviations in the actions than a finite difference technique. On the 6 Dec 2017 In the context of string theory this action is also a world sheet description of a particular tachyonic background. This has been exploited in. operator of the model in terms of the Sine-Gordon field of the Coulomb gas and hence obtain a dual monopoles [5] which have zero size and infinite action. 18 Sep 2014 We introduce the dynamical sine-Gordon equation in two space dimensions with parameter by the action of Π onto the symbols Ξk a and Ξk. E. Application I - The sine-Gordon model re-scaled action 18.

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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, and rediscovered by Frenkel and Kontorova (1939) in their study of crystal dislocations known as the Frenkel–Kontorova 2006-12-01 · The construction of the action variable for the sine–Gordon model The sine–Gordon model has infinitely many local conserved charges, which are in involution with each other. Therefore each solution ϕ ( τ , σ ) defines an infinite-dimensional “invariant torus” which is defined as the orbit of ϕ ( τ , σ ) under the Hamiltonian flows generated by the local conserved charges. The designation “sine-Gordon” is also used for various equations that generalize [1] or bear resemblance to it.

### We propose an action for a sine-Gordon-like theory, which reproduces the classical equations of motion of the Green-Schwarz-Metsaev-Tseytlin superstring on AdS 5 × S 5. The action is relativistically invariant. It is a mass-deformed gauged WZW model for SO(4, 1) × SO(5)/SO(4) × SO(4) interacting with fermions.

YouTube Kids provides a more contained environment for kids to explore YouTube and makes it easier for parents and caregivers to guide their journey. This project deals with creating a numerical solver of the sine-Gordon equation using the summation- by- parts and simultaneous approximation term method in combination with a finite difference tim Teitelboim(JT) dilaton gravity and solitons in sine-Gordon field theory is described. In order to derive this from an action principle, one needs to introduce an.

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Such solutions are analytic in the spatial variable x and the temporal variable t, and they are exponentially asymptotic to integer multiples of 2π as x → ±∞.

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### The Hamiltonian version of the sine-Gordon equation (in case (1), for example) is the Hamiltonian system with Hamiltonian. P 0 = 1 γ ∫ − ∞ + ∞ ( 1 2 π 2 ( x) − 1 2 ( ∂ u ∂ x) 2 + m 2 ( 1 − cos. . u)) d x, γ > 0, and symplectic form. Ω = 1 γ ∫ − ∞ + ∞ d π ( x) ∧ d u ( x) d x, π = ∂ u ∂ t.

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## This project deals with creating a numerical solver of the sine-Gordon equation using the summation- by- parts and simultaneous approximation term method in combination with a finite difference tim

Wiss. (Muench.), Vol. 40, pp View the profiles of people named Gordon Sine. Join Facebook to connect with Gordon Sine and others you may know. Facebook gives people the power to What is the abbreviation for Discrete Sine-Gordon? What does DSG stand for? DSG abbreviation stands for Discrete Sine-Gordon. sine gordon.

SUMMARY OF THE LECTURES. Lecture 2. January 21st. Renormalization Group Theory .