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The sine-Gordon equation,. 8'u/8T' —&'u/BX'+ sin(u) Sine-Gordon equation The sine-Gordon equation is a nonlinear hyperbolic partial differential equation in 1 + 1 dimensions involving the d'Alembert operator and Motion of a driven and heavily damped sine-Gordon chain with a low density of kinks and tight coupling between particles is controlled by the nucleation an. May 28, 2015 The (1+1)-dimensional Sine-Gordon equation passes integrability tests commonly applied to nonlinear evolution equations. Its kink solutions Exact Solutions > Nonlinear Partial Differential Equations >. Second-Order Hyperbolic Partial Differential Equations > Sine-Gordon Equation.

The Sine Gordon Equation. In[1]:= Clear "Global' ". The Equation. The equation is . 2 u x2. 2 u t2 sin u.

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Indeed, using our criterion, we prove that the massive continuum sine‐Gordon model with β < 6π satisfies asymptotically optimal log‐Sobolev inequalities for Glauber and Kawasaki dynamics. These dynamics can be For $0<β<6π$, we prove that the distribution of the centred maximum of the $ε$-regularised continuum sine-Gordon field on the two-dimensional torus converges to a randomly shifted Gumbel distribution as $ε\\to 0$.

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[12] is equivalent to the sine-Gordon equation uv = sin . Extension of constant negative curvature surfaces. The advantage of (6.7) is that it is valid even if 0 (mod ). Thus, we have Sect. 6 (20160527) 46 Theorem 6.8. Let : D ! R 3 be a smooth function on an simply connected domain D in the uv -plane satisfying the sine-Gordon equation (6.3) .

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At low T both junctions exhibit a conventional behavior, described by the local sine-Gordon equation. However, at elevated T the behavior becomes qualitatively you toJin Qua, Gordon?

9. kink - A fit of coughing or laughter.
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Renormalization group flows equations of the sine Sine-Gordon Model. From 1D interacting electrons to the sine-Gordon model: Schematics of bosonization. Bosonized. low-energy full . H. in the charge and spin-basis: Free bosons-theory for the charge mode. Sine-Gordon model for the spin mode.