The Wronskian solutions to the sine–Gordon (sG) equation that can provide interaction of different kinds are revisited. And a novel expression N-soliton solution with nonzero background sG is presented. kinks (solitons), breathers and interactions among solitons also derived directly from expression. Due existences abundant structures breathers, it possible search for coherent structures, or bo...

We study the sine-Gordon model in two dimensional space time in two different domains. For β > 8π and weak coupling, we introduce an ultraviolet cutoff and study the infrared behavior. A renormalization group analysis shows that the the model is asymptotically free in the infrared. For β < 8π and weak coupling, we introduce an infrared cutoff and study the ultraviolet behavior. A renormalizatio...

We study the evolution of fronts in a nonlinear wave equation with global feedback. This equation generalizes the Klein-Gordon and sine-Gordon equations. Extending previous work, we describe the derivation of an equation governing the front motion, which is strongly nonlinear, and, for the two-dimensional case, generalizes the damped Born-Infeld equation. We study the motion of one- and two-dim...

An useful strategy for the study of nonlinear partial differential equations (PDE) arising in pattern formation is to consider asymptotic solutions containing one or several localized defects and to simplify the dynamics by finding the equations of motion of the system of interacting defects. The great advantage of this approach is that we are dealing with ordinary differential equations (ODEs)...