This item is available under a Creative Commons License for non-commercial use only
We study extensions of N-wave systems with PT-symmetry. The types of (nonlocal) reductions leading to integrable equations invariant with respect to P- (spatial reflection) and T- (time reversal) symmetries is described. The corresponding constraints on the fundamental analytic solutions and the scattering data are derived. Based on examples of 3-wave (related to the algebra sl(3,C)) and 4-wave (related to the algebra so(5,C)) systems, the properties of different types of 1- and 2-soliton solutions are discussed. It is shown that the PT symmetric 3-wave equations may have regular multi-soliton solutions for some specific choices of their parameters.
Gerdjikov, V.S., Grahovski, G.G. & Ivanov, R.I. (2016) On the N-wave Equations with PT-symmetry. Theoretical and mathematical physics (2016) 188: 1305-1321. doi:10.1134/S0040577916090038