Harmonic maps X:(S,h) --> N from a 2-manifold S with indefinite metric h to a semi-Riemannian manifold N are characterized, assuming that the induced metric I is nondegenerate. Except in one very special case, the characterizations involve a canonically determined holomorphic quadratic differential on a naturally chosen conformal structure. This is surprising because the Euler-Lagrange equation...

A continuous sequence of infinitesimal unitary transformations is used to diagonalize the quantum sine-Gordon model for β2 ∈ (2π,∞). This approach can be understood as an extension of perturbative scaling theory since it links weakto strong-coupling behavior in a systematic expansion: a small expansion parameter is identified and this parameter remains small throughout the entire flow unlike th...

The present paper deals with results of orbital instability of periodic waves related to sine-Gordon equation. Our periodic solutions obtained in our study tend to a kink wave solutions in the infinite wavelength scenario. The approaches used here will be the classical Grillakis, Shatah and Strauss’ theory.

In Phys. Rev. B 42, 2290 (1990) we used a rigorous projection operator collective variable formalism for nonlinear Klein-Gordon equations to prove the continuum sine-Gordon (SG) equation has a long lived quasimode whose frequency is in the continuum just above the lower phonon band edge with a lifetime . We confirmed the analytic calculations by simulations which agreed very closely with the an...