Recent results using inverse scattering techniques interpret every solution φ(x, y) of the sine-Gordon equation as a non-linear superposition of solutions along the axes x = 0 and y = 0. This has a well-known geometric interpretation, namely that every weakly regular surface of Gauss curvature K = −1, in arc length asymptotic line parametrization, is uniquely determined by the values φ(x, 0) an...

X iv :h ep -t h/ 94 09 09 7v 1 1 7 Se p 19 94 CALT-68-1949, USC-94-015 hep-th/9409097 September 1994 On the non-relativistic limit of the quantum sine-Gordon model with integrable boundary condition. A. Kapustin, S. Skorik † Physics Department, California Institute of Technology, Pasadena, CA 91125. ‡ Physics Department, University of Southern California, Los Angeles, CA 90089-0484. Abstract We...

In this paper we study the dynamics of explicit solutions $2+1$-dimensional ($2$D) sine-Gordon equation. The Darboux transformation is applied to associated linear eigenvalue problem construct nontrivial $2$D equation in terms ratios determinants. We obtained a generalized expression for $N$-fold transformed dynamical variable which enables us calculate expressions solutions. order explore kink...

We investigate the interface coupling between the 2D sine-Gordon equation and the 2D wave equation in the context of a Josephson window junction using a finite volume numerical method and soliton perturbation theory. The geometry of the domain as well as the electrical coupling parameters are considered. When the linear region is located at each end of the nonlinear domain, we derive an effecti...

The renormalization group (RG) flow for the two-dimensional sine-Gordon model is determined by means of Polchinski's RG equation at next-to-leading order in the derivative expansion. In this work we have two different goals, (i) to consider the renormalization scheme-dependence of Polchinski's method by matching Polchinski's equation with the Wegner-Houghton equation and with the real space RG ...

We extend the notion of space shifts introduced in [FV3] for certain quantum light cone lattice equations of sine-Gordon type at root of unity (e.g. [FV1][FV2][BKP][BBR]). As a result we obtain a compatibility equation for the roots of central elements within the algebra of observables (also called current algebra). The equation which is obtained by exponentiating these roots is exactly the evo...

This work studies the damped double sine-Gordon equation driven by a biharmonic force, where a parameter lambda controls the existence and the frequency of an internal mode. The role of internal oscillations of the kink width in ratchet dynamics of kink is investigated within the framework of collective coordinate theories. It is found that the ratchet velocity of the kink, when an internal mod...

We generalize the approach first proposed by Manton [Nucl. Phys. B 150, 397 (1979)] to compute solitary wave interactions in translationally invariant, dispersive equations that support such localized solutions. The approach is illustrated using as examples solitons in the Korteweg-de Vries equation, standing waves in the nonlinear Schrödinger equation, and kinks as well as breathers of the sin...