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Teoreticheskaya i Matematicheskaya Fizika, 1988, Volume 77, Number 1, Pages 60–76 (Mi tmf5683)  

Gauge transformation and generating operators for a quadratic bundle

I. S. Vaklev, M. I. Ivanov
References:
Abstract: A gauge-covariant formulation of the theory of the generating operator $\Lambda$ for a quadratic bundle is found. On this basis, the method of expansion with respect to “squared solutions” is applied to the auxiliary linear problem
$$ \left\{iS_0(x)\frac{d}{dx}+\lambda S_1(x)-\lambda^2\right\}\tilde v(x,\lambda)=0. $$
Thus, for nonlinear evolution equations associated with this problem a hierarchy of Hamiltonian structures is obtained and their complete integrability is proved. Some examples, including equations of Landau–Lifshitz type, are considered for suitable reduction.
Received: 18.03.1987
English version:
Theoretical and Mathematical Physics, 1988, Volume 77, Issue 1, Pages 1044–1055
DOI: https://doi.org/10.1007/BF01028679
Bibliographic databases:
Language: Russian
Citation: I. S. Vaklev, M. I. Ivanov, “Gauge transformation and generating operators for a quadratic bundle”, TMF, 77:1 (1988), 60–76; Theoret. and Math. Phys., 77:1 (1988), 1044–1055
Citation in format AMSBIB
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\by I.~S.~Vaklev, M.~I.~Ivanov
\paper Gauge transformation and generating operators for a~quadratic bundle
\jour TMF
\yr 1988
\vol 77
\issue 1
\pages 60--76
\mathnet{http://mi.mathnet.ru/tmf5683}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=972481}
\transl
\jour Theoret. and Math. Phys.
\yr 1988
\vol 77
\issue 1
\pages 1044--1055
\crossref{https://doi.org/10.1007/BF01028679}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1988AD89600006}
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    Теоретическая и математическая физика Theoretical and Mathematical Physics
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