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Teoreticheskaya i Matematicheskaya Fizika, 1988, Volume 77, Number 1, Pages 60–76
(Mi tmf5683)
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Gauge transformation and generating operators for a quadratic bundle
I. S. Vaklev, M. I. Ivanov
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
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
Linking options:
https://www.mathnet.ru/eng/tmf5683 https://www.mathnet.ru/eng/tmf/v77/i1/p60
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Abstract page: | 233 | Full-text PDF : | 107 | References: | 40 | First page: | 1 |
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