Geodesic
System of equations for stimulated combination scattering
Teoretičeskaâ i matematičeskaâ fizika, Tome 156 (2008) no. 1, pp. 67-76

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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
Mots-clés : Zakharov–Shabat pair. 
@article{TMF_2008_156_1_a2,
     author = {V. A. Andreev},
     title = {System of equations for stimulated combination scattering},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {67--76},
     publisher = {mathdoc},
     volume = {156},
     number = {1},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2008_156_1_a2/}
}
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V. A. Andreev. System of equations for stimulated combination scattering. Teoretičeskaâ i matematičeskaâ fizika, Tome 156 (2008) no. 1, pp. 67-76. http://geodesic.mathdoc.fr/item/TMF_2008_156_1_a2/