Geodesic
The $N$-wave equations with $\mathcal{PT}$ symmetry
Teoretičeskaâ i matematičeskaâ fizika, Tome 188 (2016) no. 3, pp. 397-415 Cet article a éte moissonné depuis la source Math-Net.Ru

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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
Mots-clés : soliton solution. 
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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/

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