Chaotic solitons in Sine-Gordon system

We extend the constant-variation method to the case of partial differential equations. Applying the method to periodically perturbed Sine-Gordon syste m, we find some novel solitons, which are embedded in a chaotic attractor a nd possess controllable velocity of motion. Taking periodically driven long Josephson junction as an example the corresponding chaotic region in param eter space and chaotic orbit are obtained analytically and numerically.