Geodesic
Multidimensional linearizable system of $n$-wave-type equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 190 (2017) no. 1, pp. 48-57

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We propose a linearizable version of a multidimensional system of $n$-wave-type nonlinear partial differential equations (PDEs). We derive this system using the spectral representation of its solution via a procedure similar to the dressing method for nonlinear PDEs integrable by the inverse scattering transform method. We show that the proposed system is completely integrable and construct a particular solution.
Keywords: $n$-wave equation, linearizable equation, dressing method, periodic solution. 
@article{TMF_2017_190_1_a2,
     author = {A. I. Zenchuk},
     title = {Multidimensional linearizable system of $n$-wave-type equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {48--57},
     publisher = {mathdoc},
     volume = {190},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2017_190_1_a2/}
}
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A. I. Zenchuk. Multidimensional linearizable system of $n$-wave-type equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 190 (2017) no. 1, pp. 48-57. http://geodesic.mathdoc.fr/item/TMF_2017_190_1_a2/