Abstract:
Soliton-like solutions are obtained and investigated for the “perturbed” Schrödinger equation with cubic nonlinearity, which describes many phenomena in the theory of the condensed state. It is shown that there exists an entire class of solutions that cannot be obtained by the standard procedure of expansion with respect to a small parameter, this being so even in the framework of the inverse scattering technique. The explicit form of two such solutions is given, which immediately demonstrates the validity of the above assertion.
Citation:
V. G. Makhan'kov, V. K. Fedyanin, “New form of collective particle-like excitations in one-dimensional systems with resonance interaction”, TMF, 39:3 (1979), 381–392; Theoret. and Math. Phys., 39:3 (1979), 529–536
\Bibitem{MakFed79}
\by V.~G.~Makhan'kov, V.~K.~Fedyanin
\paper New form of collective particle-like excitations in one-dimensional systems with resonance interaction
\jour TMF
\yr 1979
\vol 39
\issue 3
\pages 381--392
\mathnet{http://mi.mathnet.ru/tmf2861}
\transl
\jour Theoret. and Math. Phys.
\yr 1979
\vol 39
\issue 3
\pages 529--536
\crossref{https://doi.org/10.1007/BF01018001}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1979JA61200010}
Linking options:
https://www.mathnet.ru/eng/tmf2861
https://www.mathnet.ru/eng/tmf/v39/i3/p381
This publication is cited in the following 3 articles:
F. Kh. Abdullaev, “Soliton collective excitations in stochastic molecular crystals”, Theoret. and Math. Phys., 51:3 (1982), 607–610
V. K. Fedyanin, “Particle-like excitations in systems described by the Hubbard model without the chirality condition”, Theoret. and Math. Phys., 46:1 (1981), 57–60
F. Kh. Abdullaev, A. A. Abdumalikov, A. S. Rakhmatov, “Solitons in stochastic molecular chains”, Soviet Physics Journal, 24:12 (1981), 1082
Citation in format AMSBIB
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