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System of equations for stimulated combination scattering and the related double periodic A (1) n Toda chains

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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 (1)n Toda chains is also shown to be integrable and to have a Zakharov-Shabat pair.

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Authors and Affiliations

  1. Lebedev Physical Institute, RAS, Moscow, Russia

    V. A. Andreev

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  1. V. A. Andreev
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Correspondence to V. A. Andreev.

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In memory of Leonid Aleksandrovich Shelepin

__________

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 1, pp. 67–76, July, 2008.

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Andreev, V.A. System of equations for stimulated combination scattering and the related double periodic A (1) n Toda chains. Theor Math Phys 156, 1020–1027 (2008). https://doi.org/10.1007/s11232-008-0095-7

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  • DOI: https://doi.org/10.1007/s11232-008-0095-7

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