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Teoreticheskaya i Matematicheskaya Fizika, 2017, Volume 190, Number 1, Pages 48–57
DOI: https://doi.org/10.4213/tmf9205 (Mi tmf9205) 		 
Multidimensional linearizable system of $n$-wave-type equations

A. I. Zenchuk

Institute of Problems of Chemical Physics, Russian Academy of Sciences, Chernogolovka, Moscow region
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DOI: https://doi.org/10.4213/tmf9205
Abstract: 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.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00389
Ministry of Education and Science of the Russian Federation НШ-9697.2016.2
This research is supported in part by the Russian Foundation for Basic Research (Grant No. 14-01-00389) and the Program for Supporting Leading Scientific Schools (Grant No. NSh-9697.2016.2).
Received: 01.04.2016
Revised: 15.04.2016
English version:
Theoretical and Mathematical Physics, 2017, Volume 190, Issue 1, Pages 43–51
DOI: https://doi.org/10.1134/S0040577917010032
Bibliographic databases:
Document Type: Article
PACS: 02.30.Ik,02.30.Jr
MSC: 37K10 , 37K15
Language: Russian
Citation: A. I. Zenchuk, “Multidimensional linearizable system of $n$-wave-type equations”, TMF, 190:1 (2017), 48–57; Theoret. and Math. Phys., 190:1 (2017), 43–51
Citation in format AMSBIB
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