New Variable Separated Solutions and Ghoston Structure for the (2+1)-Dimensional Sine-Gordon System

The Bäcklund transformation and variable separation approach are developed for sine-Gordon systems. Three new types of variable separated solutions with some arbitrary functions have been obtained. A new kind of ghoston structure, which is invisible at most of time and can only be detected when it meets with a foldon, is found. This new structure shows a novel interesting and mysterious phenomenon.