Construction of parity-time symmetric potential through the soliton theory

A systematic method is presented for the construction of the parity-time (PT) symmetric potentials. The key idea is the transformation between Dirac type and Schrodinger type eigenvalue problems in the inverse scattering method. As a standard example, the modified Korteweg-de Vries (mKdV) equation is considered. There exists a PT symmetric potential corresponding to a soliton solution. One- and two-soliton PT symmetric potentials are given explicitly. The extensions of the theory into other types of solutions and other soliton equations are discussed.