Speaker: Svetlana Roudenko, George Washington University
Heads and Tails in a Klein-Gordon equation
After the physicists Oskar Klein and Walter Gordon proposed in 1926 an equation that describes spinless relativistic electrons, the Klein-Gordon equation officially appeared in the quantum mechanics. On the other hand, one can view this model as a wave equation with a linear term added.
In this talk, I will discuss a nonlinear version of the Klein-Gordon equation in 3d, and explore its solutions that exist for all times vs the ones that may cease to exist in finite time. As it is related to the Schrödinger equation, we can use tools of the dispersive equations machinery to investigate singularity formations or global in time behavior. In particular, the behavior near the ground or excited states produce various interesting solutions, and as we investigate further, interesting head and tails properties appear. I will compare the theoretical and numerical results in solution behavior for this equation and comment on extensions to other nonlinearities and extensions. Parts of this work is joint with Thomas Duyckaerts and also with Kai Yang and Yanxiang Zhao.
Department of Mathematical Sciences
George Mason University
4400 University Drive, MS 3F2
Fairfax, VA 22030-4444
Tel. 703-993-1460, Fax. 703-993-1491