Exact and numerical solutions to the perturbed sine-Gordon equation (Q1071941)

The perturbed sine-Gordon equation is \[ \phi_{xx}-\phi_{tt}=\sin \phi +\alpha \phi_ t[1+\epsilon \cos \phi)+\eta. \] This models a Josphson junction of infinite length. Time is measured in inverse units of plasma frequency. The authors consider first order perturbation, determining the stationary velocity \(u_{\infty}\) of a fluxon. An unstable Kink solution obtained by the perturbation technique is compared with numerical simulation. The agreement is good.