On the N-wave Equations with PT-symmetry
Exactly Solvable and Integrable Systems
2016-10-20 v2 Mathematical Physics
math.MP
Abstract
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.
Keywords
Cite
@article{arxiv.1601.01929,
title = {On the N-wave Equations with PT-symmetry},
author = {Vladimir S. Gerdjikov and Georgi G. Grahovski and Rossen I. Ivanov},
journal= {arXiv preprint arXiv:1601.01929},
year = {2016}
}
Comments
20 pages, LaTeX