RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



TMF:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


TMF, 1987, Volume 70, Number 3, Pages 323–341 (Mi tmf4658)  

This article is cited in 22 scientific papers (total in 22 papers)

Inverse scattering method with variable spectral parameter

S. P. Burtsev, V. E. Zakharov, A. V. Mikhailov


Abstract: In the traditional scheme of the inverse scattering method the spectral parameter of the auxiliary linear problem is usually considered as a constant. The authors propose to consider it as a variable satisfying an over-determined system of differential equations which is determined by the auxiliary linear problem. Nonlinear equations arising in this approach include, as a rule, the explicit dependence on coordinates. Besides the known equations (equation of gravitation, Heisenberg equation in axial geometry etc.) the method makes it possible to construct a number of new integrable equations valuable for applications.

Full text: PDF file (1624 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 1987, 70:3, 227–240

Bibliographic databases:

Received: 06.02.1986

Citation: S. P. Burtsev, V. E. Zakharov, A. V. Mikhailov, “Inverse scattering method with variable spectral parameter”, TMF, 70:3 (1987), 323–341; Theoret. and Math. Phys., 70:3 (1987), 227–240

Citation in format AMSBIB
\Bibitem{BurZakMik87}
\by S.~P.~Burtsev, V.~E.~Zakharov, A.~V.~Mikhailov
\paper Inverse scattering method with variable spectral parameter
\jour TMF
\yr 1987
\vol 70
\issue 3
\pages 323--341
\mathnet{http://mi.mathnet.ru/tmf4658}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=894455}
\zmath{https://zbmath.org/?q=an:0639.35074}
\transl
\jour Theoret. and Math. Phys.
\yr 1987
\vol 70
\issue 3
\pages 227--240
\crossref{https://doi.org/10.1007/BF01040999}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1987K573300001}


Linking options:
  • http://mi.mathnet.ru/eng/tmf4658
  • http://mi.mathnet.ru/eng/tmf/v70/i3/p323

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. D. A. Korotkin, “Finite-gap solutions of the stationary axisymmetric Einstein equation in vacuum”, Theoret. and Math. Phys., 77:1 (1988), 1018–1031  mathnet  crossref  mathscinet  isi
    2. D. A. Korotkin, “Finite-gap solutions of self-duality equations for $SU(1,1)$ and $SU(2)$ groups and their axisymmetric stationary reductions”, Math. USSR-Sb., 70:2 (1991), 355–366  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. V. E. Adler, “Lie-algebraic approach to nonlocal symmetries of integrable systems”, Theoret. and Math. Phys., 89:3 (1991), 1239–1248  mathnet  crossref  mathscinet  zmath  isi
    4. L. V. Ryzhik, E. I. Shulman, “Symmetry algebra of nonlinear integrable equations”, Theoret. and Math. Phys., 95:1 (1993), 387–392  mathnet  crossref  mathscinet  zmath
    5. T. A. Ivanova, A. D. Popov, “Self-dual Yang–Mills fields in $d=4$ and integrable systems in $1\leq d\leq 3$”, Theoret. and Math. Phys., 102:3 (1995), 280–304  mathnet  crossref  mathscinet  zmath  isi
    6. L. A. Uvarova, V. K. Fedyanin, “Asymptotic solutions for electromagnetic wave in an optical nonlinear cylinder”, Theoret. and Math. Phys., 106:1 (1996), 68–74  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. E. Sh. Gutshabash, V. D. Lipovskii, S. S. Nikulichev, “Nonlinear $\sigma$-model in a curved space, gauge equivalence, and exact solutions of $(2+0)$-dimensional integrable equations”, Theoret. and Math. Phys., 115:3 (1998), 619–638  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    8. V. E. Adler, A. B. Shabat, R. I. Yamilov, “Symmetry approach to the integrability problem”, Theoret. and Math. Phys., 125:3 (2000), 1603–1661  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    9. A. Yu. Kokotov, D. A. Korotkin, V. Shramchenko, “Nonautonomous Integrable Systems Associated with Hurwitz Spaces in Genuses Zero and One”, Theoret. and Math. Phys., 137:1 (2003), 1485–1491  mathnet  crossref  crossref  mathscinet  zmath  isi
    10. E. Sh. Gutshabash, “On canonical variables for integrable models of magnets”, J. Math. Sci. (N. Y.), 151:2 (2008), 2865–2879  mathnet  crossref  mathscinet
    11. Matveev, VB, “30 years of finite-gap integration theory”, Philosophical Transactions of the Royal Society A-Mathematical Physical and Engineering Sciences, 366:1867 (2008), 837  crossref  isi
    12. Hao Hong-hai, Zhang Da-jun, Deng Shu-fang, “The Kadomtsev–Petviashvili equation with self-consistent sources in nonuniform media”, Theoret. and Math. Phys., 158:2 (2009), 151–166  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    13. Cieslinski, JL, “Algebraic construction of the Darboux matrix revisited”, Journal of Physics A-Mathematical and Theoretical, 42:40 (2009), 404003  crossref  isi
    14. Quantum Electron., 40:9 (2010), 756–781  mathnet  crossref  adsnasa  isi  elib
    15. Aristophanes Dimakis, Nils Kanning, Folkert Müller-Hoissen, “The Non-Autonomous Chiral Model and the Ernst Equation of General Relativity in the Bidifferential Calculus Framework”, SIGMA, 7 (2011), 118, 27 pp.  mathnet  crossref  mathscinet
    16. Su J., Xu W., Xu G., Gao L., “Negaton, positon and complexiton solutions of the nonisospectral KdV equations with self-consistent sources”, Commun Nonlinear Sci Numer Simul, 17:1 (2012), 110–118  crossref  isi
    17. Odesskii A.V., Sokolov V.V., “Non-Homogeneous Systems of Hydrodynamic Type Possessing Lax Representations”, Commun. Math. Phys., 324:1 (2013), 47–62  crossref  isi
    18. D. M. J. Calderbank, “Integrable Background Geometries”, SIGMA, 10 (2014), 034, 51 pp.  mathnet  crossref  mathscinet
    19. Comput. Math. Math. Phys., 54:4 (2014), 727–743  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    20. Morozov O.I., “The Four-Dimensional Martinez Alonso-Shabat Equation: Differential Coverings and Recursion Operators”, J. Geom. Phys., 85 (2014), 75–80  crossref  isi
    21. Bogdanov L.V. Konopelchenko B.G., “Projective Differential Geometry of Multidimensional Dispersionless Integrable Hierarchies”, Physics and Mathematics of Nonlinear Phenomena 2013, Journal of Physics Conference Series, 482, IOP Publishing Ltd, 2014, 012005  crossref  isi
    22. Sergyeyev A., “New Integrable (3+1)-Dimensional Systems and Contact Geometry”, Lett. Math. Phys., 108:2 (2018), 359–376  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
    Number of views:
    This page:531
    Full text:190
    References:46
    First page:3

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019