PT-symmetric deformations of the Korteweg-de Vries equation

We propose a new family of complex PT-symmetric extensions of the Korteweg-de Vries equation. The deformed equations can be associated to a sequence of non-Hermitian Hamiltonians. The first charges related to the conservation of mass, momentum and energy are constructed. We investigate solitary wave solutions of the equation of motion for various boundary conditions.
11 pages, 3 figures