Uspekhi Matematicheskikh Nauk
General information
Latest issue
Impact factor
License agreement
Submit a manuscript

Search papers
Search references

Latest issue
Current issues
Archive issues
What is RSS

Uspekhi Mat. Nauk:

Personal entry:
Save password
Forgotten password?

Uspekhi Mat. Nauk, 1988, Volume 43, Issue 5(263), Pages 211–212 (Mi umn2023)  

This article is cited in 24 scientific papers (total in 24 papers)

In the Moscow Mathematical Society
Communications of the Moscow Mathematical Society

Algebro-geometric construction of self-similar solutions of the Whitham equations

G. V. Potëmin

Full text: PDF file (144 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 1988, 43:5, 252–253

Bibliographic databases:

MSC: 14F43, 37K10, 74J40, 37L05
Received: 26.04.1988

Citation: G. V. Potëmin, “Algebro-geometric construction of self-similar solutions of the Whitham equations”, Uspekhi Mat. Nauk, 43:5(263) (1988), 211–212; Russian Math. Surveys, 43:5 (1988), 252–253

Citation in format AMSBIB
\by G.~V.~Pot\"emin
\paper Algebro-geometric construction of~self-similar solutions of~the~Whitham equations
\jour Uspekhi Mat. Nauk
\yr 1988
\vol 43
\issue 5(263)
\pages 211--212
\jour Russian Math. Surveys
\yr 1988
\vol 43
\issue 5
\pages 252--253

Linking options:

    SHARE: FaceBook Twitter Livejournal

    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. S. P. Tsarev, “The geometry of harniltonian systems of hydrodynamic type. The generalized hodograph method”, Math. USSR-Izv., 37:2 (1991), 397–419  mathnet  crossref  mathscinet  zmath  adsnasa
    2. V. R. Kudashev, S. E. Sharapov, “Inheritance of KdV symmetries under Whitham averaging and hydrodynamic symmetries of the Witham equations”, Theoret. and Math. Phys., 87:1 (1991), 358–363  mathnet  crossref  mathscinet  zmath  isi
    3. Fei Ran Tian, “Oscillations of the zero dispersion limit of the korteweg-de vries equation”, Comm Pure Appl Math, 46:8 (1993), 1093  crossref  mathscinet  zmath  isi
    4. Otis C. Wright, “Korteweg–de vries zero dispersion limit: Through first breaking for cubic-like analytic initial data”, Comm Pure Appl Math, 46:3 (1993), 423  crossref  mathscinet  zmath  isi
    5. Fei Ran Tian, “The initial value problem for the Whitham averaged system”, Comm Math Phys, 166:1 (1994), 79  crossref  mathscinet  zmath  isi
    6. V. Yu. Novokshenov, “Whitham Gap Dynamics of the Real-Valued Solution of the Sine-Gordon Equation with Finite-Gap Boundary Conditions”, Funct. Anal. Appl., 30:4 (1996), 246–256  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. M.C. Jorge, A.A. Minzoni, Noel F. Smyth, “Modulation solutions for the Benjamin–Ono equation”, Physica D: Nonlinear Phenomena, 132:1-2 (1999), 1  crossref
    8. T. Grava, “Existence of a global solution of the Whitham equations”, Theoret. and Math. Phys., 122:1 (2000), 46–57  mathnet  crossref  crossref  mathscinet  zmath  isi
    9. Gennady A. El, Alexander L. Krylov, Stephanos Venakides, “Unified approach to KdV modulations”, Comm Pure Appl Math, 54:10 (2001), 1243  crossref  mathscinet  zmath  isi  elib
    10. Grava, T, “Asymptotic solutions of the Whitham equations”, Journal of Nonlinear Mathematical Physics, 8 (2001), 128  crossref  mathscinet  zmath  adsnasa  isi
    11. Tamara Grava, Fei-Ran Tian, “The generation, propagation, and extinction of multiphases in the KdV zero-dispersion limit”, Comm Pure Appl Math, 55:12 (2002), 1569  crossref  mathscinet  zmath  isi
    12. A. M. Kamchatnov, R. A. Kraenkel, B. A. Umarov, “Asymptotic soliton train solutions of the defocusing nonlinear Schrödinger equation”, Phys Rev E, 66:3 (2002), 036609  crossref  mathscinet  adsnasa  isi
    13. Eldad Bettelheim, Oded Agam, Anton Zabrodin, Paul Wiegmann, “Singularities of the Hele-Shaw Flow and Shock Waves in Dispersive Media”, Phys Rev Letters, 95:24 (2005), 244504  crossref  isi
    14. A. Ya. Maltsev, “Whitham systems and deformations”, J Math Phys (N Y ), 47:7 (2006), 073505  crossref  mathscinet  zmath  adsnasa  isi
    15. A Ya Maltsev, “The conservation of the Hamiltonian structures in the deformations of the Whitham systems”, J Phys A Math Theor, 43:6 (2010), 065202  crossref  mathscinet  zmath  adsnasa  elib
    16. T Claeys, “Asymptotics for a special solution to the second member of the Painlevé I hierarchy”, J Phys A Math Theor, 43:43 (2010), 434012  crossref
    17. Garifullin R., Suleimanov B., Tarkhanov N., “Phase shift in the Whitham zone for the Gurevich-Pitaevskii special solution of the Korteweg-de Vries equation”, Physics Letters A, 374:13–14 (2010), 1420–1424  crossref  isi  elib
    18. Tom Claeys, “Pole-free solutions of the first Painlevé hierarchy and non-generic critical behavior for the KdV equation”, Physica D: Nonlinear Phenomena, 2011  crossref
    19. B. I. Suleimanov, “Asymptotics of the Gurevich–Pitaevskii universal special solution of the Korteweg–de Vries equation as $|x|\to\infty$”, Proc. Steklov Inst. Math. (Suppl.), 281, suppl. 1 (2013), 137–145  mathnet  crossref  isi  elib
    20. B. Dubrovin, A. Kapaev, “On an isomonodromy deformation equation without the Painlevé property”, Russ. J. Math. Phys, 21:1 (2014), 9  crossref
    21. B. I. Suleimanov, ““Quantizations” of Higher Hamiltonian Analogues of the Painlevé I and Painlevé II Equations with Two Degrees of Freedom”, Funct. Anal. Appl., 48:3 (2014), 198–207  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    22. Rustem R. Aydagulov, Alexander A. Minakov, “Initial-Boundary Value Problem for Stimulated Raman Scattering Model: Solvability of Whitham Type System of Equations Arising in Long-Time Asymptotic Analysis”, SIGMA, 14 (2018), 119, 19 pp.  mathnet  crossref
    23. A. M. Kamchatnov, “Gurevich–Pitaevskii problem and its development”, Phys. Usp., 64:1 (2021), 48–82  mathnet  crossref  crossref  isi  elib
    24. B. I. Suleimanov, A. M. Shavlukov, “Integrable Abel equation and asymptotics of symmetry solutions of Korteweg-de Vries equation”, Ufa Math. J., 13:2 (2021), 99–106  mathnet  crossref  isi
  • Успехи математических наук Russian Mathematical Surveys
    Number of views:
    This page:284
    Full text:106
    First page:1

    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021