Abstract:
The solutions of the quantum Gel' fand–Levitan–Marehenko equations for the sine-Gordon model are studied in the sector containing solitons. The case γ=π/ν (ν integer), when there is no soliton reflection, is considered. A recursive procedure for constructing solutions is obtained, and examples in sectors containing a small number of solitons are considered.
Citation:
F. A. Smirnov, “Solution of quantum Gel'fand–Levitan–Marchenko equations for the sine-gordon model in the soliton sector for γ=π/ν”, TMF, 67:1 (1986), 40–51; Theoret. and Math. Phys., 67:1 (1986), 344–351
\Bibitem{Smi86}
\by F.~A.~Smirnov
\paper Solution of quantum Gel'fand--Levitan--Marchenko equations for the sine-gordon model in the soliton sector for $\gamma=\pi/\nu$
\jour TMF
\yr 1986
\vol 67
\issue 1
\pages 40--51
\mathnet{http://mi.mathnet.ru/tmf4919}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=843798}
\transl
\jour Theoret. and Math. Phys.
\yr 1986
\vol 67
\issue 1
\pages 344--351
\crossref{https://doi.org/10.1007/BF01028887}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1986E968100005}
Linking options:
https://www.mathnet.ru/eng/tmf4919
https://www.mathnet.ru/eng/tmf/v67/i1/p40
This publication is cited in the following 5 articles:
Karol K. Kozlowski, “On convergence of form factor expansions in the infinite volume quantum Sinh-Gordon model in 1+1 dimensions”, Invent. math., 233:2 (2023), 725
J.M. Maillet, V. Terras, “On the quantum inverse scattering problem”, Nuclear Physics B, 575:3 (2000), 627
V.A. Fateev, E. Onofri, Al.B. Zamolodchikov, “Integrable deformations of the O(3) sigma model. The sausage model”, Nuclear Physics B, 406:3 (1993), 521
A. M. Tsvelik, “Spectrum of magnetic excitations in the spin-Peierls state”, Phys. Rev. B, 45:1 (1992), 486
F. A. Smirnov, “Solution of quantum Gel'fand–Levitan–Marchenko equations for the sine-Gordon model with γ=π/ν”, Theoret. and Math. Phys., 71:3 (1987), 577–584
Citation in format AMSBIB
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