PT symmetry implies real energy and linear stability of complex soliton
Takanobu Taira
U. Tokyo

I will show that the anti-linear symmetry (PT-symmetry) of the generic complex one soliton solution implies its real energy and linear stability. Furthermore, a linear stability analysis of classical soliton solution is reduced to an auxiliary Sturm-Liouville equation, where it is equivalent to the Schroedinger equation of a PT-symmetric quantum mechanics. As a simple example, a complex sine-Gordon kink is considered.