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TMF, 2008, Volume 156, Number 1, Pages 67–76 (Mi tmf6230)  

System of equations for stimulated combination scattering and the related double periodic $A_n^{(1)}$ Toda chains

V. A. Andreev

P. N. Lebedev Physical Institute, Russian Academy of Sciences

Abstract: We consider a system of equations describing stimulated combination scattering of light. We show that solutions of this system are expressed in terms of two solutions of the sine-Gordon equation that are related to each other by a Bäcklund transformation. We also show that this system is integrable and admits a Zakharov–Shabat pair. In the general case, the system of equations for the Bäcklund transformation of periodic $A_n^{(1)}$ Toda chains is also shown to be integrable and to have a Zakharov–Shabat pair.

Keywords: combination scattering, Toda chain, Bäcklund transformation, Zakharov–Shabat pair

DOI: https://doi.org/10.4213/tmf6230

Full text: PDF file (393 kB)
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English version:
Theoretical and Mathematical Physics, 2008, 156:1, 1020–1027

Bibliographic databases:

Received: 29.03.2007
Revised: 22.06.2007

Citation: V. A. Andreev, “System of equations for stimulated combination scattering and the related double periodic $A_n^{(1)}$ Toda chains”, TMF, 156:1 (2008), 67–76; Theoret. and Math. Phys., 156:1 (2008), 1020–1027

Citation in format AMSBIB
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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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