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Teoreticheskaya i Matematicheskaya Fizika, 2000, Volume 122, Number 1, Pages 118–127
DOI: https://doi.org/10.4213/tmf559 (Mi tmf559) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Asymptotic approximations for a new eigenvalue in linear problems without a threshold

D. E. Pelinovsky, C. Sulem

University of Toronto
Full-text PDF (204 kB) Citations (8)
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DOI: https://doi.org/10.4213/tmf559
Abstract: We study the criterion for a new eigenvalue to appear in the linear spectral problem associated with the intermediate long-wave equation. We compute the asymptotic value of the new eigenvalue in the limit of a small potential using a Fourier decomposition method. We compare the results with those for the Schrödinger operator with a radially symmetrical potential.
English version:
Theoretical and Mathematical Physics, 2000, Volume 122, Issue 1, Pages 98–106
DOI: https://doi.org/10.1007/BF02551173
Bibliographic databases:
Language: Russian
Citation: D. E. Pelinovsky, C. Sulem, “Asymptotic approximations for a new eigenvalue in linear problems without a threshold”, TMF, 122:1 (2000), 118–127; Theoret. and Math. Phys., 122:1 (2000), 98–106
Citation in format AMSBIB
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\paper Asymptotic approximations for a new eigenvalue in linear problems without a threshold
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\pages 118--127
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\jour Theoret. and Math. Phys.
\yr 2000
\vol 122
\issue 1
\pages 98--106
\crossref{https://doi.org/10.1007/BF02551173}
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Linking options:
  • https://www.mathnet.ru/eng/tmf559
  • https://doi.org/10.4213/tmf559
  • https://www.mathnet.ru/eng/tmf/v122/i1/p118
    • This publication is cited in the following 8 articles:
    1. D. E. Pelinovsky, Atomic, Optical, and Plasma Physics, 45, Emergent Nonlinear Phenomena in Bose-Einstein Condensates, 2008, 377  crossref
    2. Wang, JD, “Two-dimensional defect modes in optically induced photonic lattices”, Physical Review A, 76:1 (2007), 013828  crossref  adsnasa  isi  elib  scopus  scopus  scopus
    3. A. R. Bikmetov, R. R. Gadyl'shin, “On the spectrum of the Schrödinger operator with large potential concentrated on a small set”, Math. Notes, 79:5 (2006), 729–733  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. D. I. Borisov, R. R. Gadyl'shin, “The spectrum of the Schrödinger operator with a rapidly oscillating compactly supported potential”, Theoret. and Math. Phys., 147:1 (2006), 496–500  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. A. R. Bikmetov, D. I. Borisov, “Discrete Spectrum of the Schrodinger Operator Perturbed by a Narrowly Supported Potential”, Theoret. and Math. Phys., 145:3 (2005), 1691–1702  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. R. R. Gadyl'shin, “Local Perturbations of the Schrödinger Operator on the Plane”, Theoret. and Math. Phys., 138:1 (2004), 33–44  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    7. Matsuno, Y, “Dark soliton generation for the intermediate nonlinear Schrodinger equation”, Journal of Mathematical Physics, 43:2 (2002), 984  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    8. Pelinovsky, DE, “Eigenfunctions and eigenvalues for a scalar Riemann–Hilbert problem associated to inverse scattering”, Communications in Mathematical Physics, 208:3 (2000), 713  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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