Collisions of a light bullet with kinks and standing breathers in the two-dimensional sine-Gordon equation

Abstract

The (2+1)-dimension Klein-Gordon generalised equation is numerically solved through the finite differences method. Only the sine-Gordon case is focused: kink and antikink solutions are obtained in cartesian coordinates and evidence of interaction in kink-kink collision is looked for in propagation velocity. Then the change of shape in light bullet solutions is quantified during propagation and in head-on collision. Lastly, the robustness of light bullets is verified in head-on collisions with kink, antikink, standing kink and standing breather. A 30o-collision between a light bullet and a standing kink is simulated as well.