Geodesic
The~$N$-wave equations with $\mathcal{PT}$ symmetry
Teoretičeskaâ i matematičeskaâ fizika, Tome 188 (2016) no. 3, pp. 397-415

Voir la notice de l'article provenant de la source Math-Net.Ru

We study extensions of $N$-wave systems with $\mathcal{PT}$ symmetry and describe the types of (nonlocal) reductions leading to integrable equations invariant under the $\mathcal P$ (spatial reflection) and $\mathcal T$ (time reversal) symmetries. We derive the corresponding constraints on the fundamental analytic solutions and the scattering data. Based on examples of three-wave and four-wave systems (related to the respective algebras $sl(3,\mathbb C)$) and $so(5,\mathbb C)$), we discuss the properties of different types of one- and two-soliton solutions. We show that the $\mathcal{PT}$-symmetric three-wave equations can have regular multisoliton solutions for some specific choices of their parameters.
Keywords: integrable system, $\mathcal{PT}$ symmetry, inverse scattering transform, soliton solution. 
@article{TMF_2016_188_3_a2,
     author = {V. S. Gerdjikov and G. G. Grahovski and R. I. Ivanov},
     title = {The~$N$-wave equations with $\mathcal{PT}$ symmetry},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {397--415},
     publisher = {mathdoc},
     volume = {188},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2016_188_3_a2/}
}
TY  - JOUR
AU  - V. S. Gerdjikov
AU  - G. G. Grahovski
AU  - R. I. Ivanov
TI  - The~$N$-wave equations with $\mathcal{PT}$ symmetry
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2016
SP  - 397
EP  - 415
VL  - 188
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2016_188_3_a2/
LA  - ru
ID  - TMF_2016_188_3_a2
ER  - 
%0 Journal Article
%A V. S. Gerdjikov
%A G. G. Grahovski
%A R. I. Ivanov
%T The~$N$-wave equations with $\mathcal{PT}$ symmetry
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2016
%P 397-415
%V 188
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2016_188_3_a2/
%G ru
%F TMF_2016_188_3_a2
V. S. Gerdjikov; G. G. Grahovski; R. I. Ivanov. The~$N$-wave equations with $\mathcal{PT}$ symmetry. Teoretičeskaâ i matematičeskaâ fizika, Tome 188 (2016) no. 3, pp. 397-415. http://geodesic.mathdoc.fr/item/TMF_2016_188_3_a2/