On the N-wave Equations with PT-symmetry
Preprint
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
All Related Versions
This publication has 27 references indexed in Scilit:
- Observation of parity–time symmetry in opticsNature Physics, 2010
- A Dressing Method in Mathematical Physics2007
- On the dressing method for the generalised Zakharov–Shabat systemNuclear Physics B, 2004
- Pseudo-Hermiticity and generalized PT- and CPT-symmetriesJournal of Mathematical Physics, 2003
- Isoparametric hypersurfaces in spheres, integrable nondiagonalizable systems of hydrodynamic type, and N-wave systemsDifferential Geometry and its Applications, 1995
- Scattering and inverse scattering for first order systemsCommunications on Pure and Applied Mathematics, 1984
- The generating operator for the n × n linear systemPhysica D: Nonlinear Phenomena, 1981
- A Method for Solvithe Separable Initial‐Value Problem of the Full Three‐Dimensional Three‐Wave InteractionStudies in Applied Mathematics, 1980
- The Three‐Wave Interaction—A Nondispersive PhenomenonStudies in Applied Mathematics, 1976
- Inverse-scattering problem for a system of differential equationsFunctional Analysis and Its Applications, 1975