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This article is cited in 2 scientific papers (total in 2 papers)
A New Class of Reflectionless Second-order $\mathrm{A} \Delta \mathrm{Os}$ and Its Relation to Nonlocal Solitons
S. N. M. Ruijsenaars Centre for Mathematics and Computer Science,
P.O.Box 94079, 1090 GB Amsterdam, The Netherlands
Abstract:
We study an extensive class of second-order analytic difference operators admitting reflectionless eigenfunctions. The eigenvalue equation for our $\mathrm{A} \Delta \mathrm{Os}$may be viewed as an analytic analog of a discrete spectral problem studied by Shabat. Moreover, the nonlocal soliton evolution equation we associate to the $\mathrm{A} \Delta \mathrm{Os}$ is an analytic version of a discrete equation Boiti and coworkers recently associated to Shabat's problem. We show that our nonlocal solitons $G(x,t)$ are positive for $(x,t) \in \mathbb{R}^2$ and obtain evidence that the corresponding $\mathrm{A} \Delta \mathrm{Os}$ can be reinterpreted as self-adjoint operators on $L^2(\mathbb{R},dx)$. In a suitable scaling limit the KdV solitons and reflectionless Schrodinger operators arise.
Received: 17.03.2002
Citation:
S. N. M. Ruijsenaars, “A New Class of Reflectionless Second-order $\mathrm{A} \Delta \mathrm{Os}$ and Its Relation to Nonlocal Solitons”, Regul. Chaotic Dyn., 7:4 (2002), 351–391
Linking options:
https://www.mathnet.ru/eng/rcd824 https://www.mathnet.ru/eng/rcd/v7/i4/p351
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