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Funktsional. Anal. i Prilozhen., 1980, Volume 14, Issue 2, Pages 15–24 (Mi faa1795)  

This article is cited in 42 scientific papers (total in 42 papers)

Benney equations and quasiclassical approximation in the method of the inverse problem

V. E. Zakharov


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English version:
Functional Analysis and Its Applications, 1980, 14:2, 89–98

Bibliographic databases:

UDC: 517.9
Received: 17.12.1979

Citation: V. E. Zakharov, “Benney equations and quasiclassical approximation in the method of the inverse problem”, Funktsional. Anal. i Prilozhen., 14:2 (1980), 15–24; Funct. Anal. Appl., 14:2 (1980), 89–98

Citation in format AMSBIB
\Bibitem{Zak80}
\by V.~E.~Zakharov
\paper Benney equations and quasiclassical approximation in the method of the inverse problem
\jour Funktsional. Anal. i Prilozhen.
\yr 1980
\vol 14
\issue 2
\pages 15--24
\mathnet{http://mi.mathnet.ru/faa1795}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=575201}
\zmath{https://zbmath.org/?q=an:0434.35084|0453.35086}
\transl
\jour Funct. Anal. Appl.
\yr 1980
\vol 14
\issue 2
\pages 89--98
\crossref{https://doi.org/0.1007/BF01086549}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. P. Tsarev, “On the Liouville Poisson brackets and one-dimensional Hamiltonian systems of hydrodynamic type arising in the Bogolyubov–Whitham averaging theory”, Russian Math. Surveys, 39:6 (1984), 227–228  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. V. V. Geogdzhaev, “Solution of the Benney equations by the inverse scattering method”, Theoret. and Math. Phys., 73:2 (1987), 1198–1204  mathnet  crossref  mathscinet  zmath  isi
    3. M. V. Pavlov, “Hamiltonian formalism of weakly nonlinear hydrodynamic systems”, Theoret. and Math. Phys., 73:2 (1987), 1242–1245  mathnet  crossref  zmath  isi
    4. B. A. Dubrovin, S. P. Novikov, “Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory”, Russian Math. Surveys, 44:6 (1989), 35–124  mathnet  crossref  mathscinet  zmath  adsnasa
    5. I. M. Krichever, “Spectral theory of two-dimensional periodic operators and its applications”, Russian Math. Surveys, 44:2 (1989), 145–225  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. 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
    7. M. V. Pavlov, S. P. Tsarev, “On conservation laws of Benney equations”, Russian Math. Surveys, 4:4 (1991), 196–197  mathnet  crossref  mathscinet  zmath
    8. O. I. Mokhov, “Symplectic and Poisson structures on loop spaces of smooth manifolds, and integrable systems”, Russian Math. Surveys, 53:3 (1998), 515–622  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    9. B. G. Konopelchenko, L. Martínez Alonso, E. Medina, “Quasiconformal Mappings and Solutions of the Dispersionless KP Hierarchy”, Theoret. and Math. Phys., 133:2 (2002), 1529–1538  mathnet  crossref  crossref  mathscinet  isi  elib
    10. M. V. Pavlov, S. P. Tsarev, “Tri-Hamiltonian Structures of Egorov Systems of Hydrodynamic Type”, Funct. Anal. Appl., 37:1 (2003), 32–45  mathnet  crossref  crossref  mathscinet  zmath  isi
    11. V. M. Buchstaber, D. V. Leikin, M. V. Pavlov, “Egorov Hydrodynamic Chains, the Chazy Equation, and $SL(2,\mathbb{C})$”, Funct. Anal. Appl., 37:4 (2003), 251–262  mathnet  crossref  crossref  mathscinet  zmath  isi
    12. L. V. Bogdanov, B. G. Konopelchenko, L. Martínez Alonso, “Semiclassical $\bar\partial$-Method: Generating Equations for Dispersionless Integrable Hierarchies”, Theoret. and Math. Phys., 134:1 (2003), 39–46  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    13. M. V. Pavlov, “Classifying Integrable Egoroff Hydrodynamic Chains”, Theoret. and Math. Phys., 138:1 (2004), 45–58  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    14. L. V. Bogdanov, B. G. Konopelchenko, A. Moro, “Symmetry constraints for real dispersionless Veselov–Novikov equation”, J. Math. Sci., 136:6 (2006), 4411–4418  mathnet  crossref  mathscinet  zmath  elib  elib
    15. Pavlov, MV, “The Kupershmidt hydrodynamic chains and lattices”, International Mathematics Research Notices, 2006, 46987  isi
    16. Baldwin, S, “Genus 4 trigonal reduction of the Benney equations”, Journal of Physics A-Mathematical and General, 39:14 (2006), 3607  crossref  isi
    17. M. V. Pavlov, “Integrability of the Egorov systems of hydrodynamic type”, Theoret. and Math. Phys., 150:2 (2007), 225–243  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    18. B. G. Konopelchenko, F. Magri, “Dispersionless integrable equations as coisotropic deformations: Extensions and reductions”, Theoret. and Math. Phys., 151:3 (2007), 803–819  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    19. Ferapontov, EV, “Differential-geometric approach to the integrability of hydrodynamic chains: the Haantjes tensor”, Mathematische Annalen, 339:1 (2007), 61  crossref  isi
    20. Amitava Choudhuri, B. Talukdar, U. Das, “Lagrangian Approach to Dispersionless KdV Hierarchy”, SIGMA, 3 (2007), 096, 11 pp.  mathnet  crossref  mathscinet  zmath
    21. J. Appl. Industr. Math., 4:1 (2010), 24–34  mathnet  crossref  mathscinet
    22. A. V. Odesskii, M. V. Pavlov, V. V. Sokolov, “Classification of integrable Vlasov-type equations”, Theoret. and Math. Phys., 154:2 (2008), 209–219  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    23. J. Appl. Industr. Math., 4:3 (2010), 318–331  mathnet  crossref  mathscinet
    24. Chesnokov A.A., Lyapidevskii V.Yu., “Volnovye dvizheniya idealnoi zhidkosti v uzkom otkrytom kanale”, Prikladnaya mekhanika i tekhnicheskaya fizika, 50:2 (2009), 61–71
    25. Lyapidevskii V.Yu., Chesnokov A.A., “Dokriticheskie i sverkhkriticheskie gorizontalno-sdvigovye techeniya v otkrytom kanale peremennogo secheniya”, Izv. RAN. Mekhanika zhidkosti i gaza, 2009, no. 6, 123–138
    26. Gibbons J., Lorenzoni P., Raimondo A., “Purely nonlocal Hamiltonian formalism for systems of hydrodynamic type”, J Geom Phys, 60:9 (2010), 1112–1126  crossref  isi
    27. V. V. Kozlov, “Kineticheskoe uravnenie Vlasova, dinamika sploshnykh sred i turbulentnost”, Nelineinaya dinam., 6:3 (2010), 489–512  mathnet  elib
    28. B. G. Konopelchenko, L. Martínez Alonso, E. Medina, “Singular sectors of the one-layer Benney and dispersionless Toda systems and their interrelations”, Theoret. and Math. Phys., 168:1 (2011), 963–973  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    29. Khe A.K., Chesnokov A.A., “Rasprostranenie nelineinykh vozmuschenii v kvazineitralnoi besstolknovitelnoi plazme”, Prikladnaya mekhanika i tekhnicheskaya fizika, 52:5 (2011), 3–16  elib
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    31. Konopelchenko B.G. Ortenzi G., “Quasi-Classical Approximation in Vortex Filament Dynamics. Integrable Systems, Gradient Catastrophe, and Flutter”, Stud. Appl. Math., 130:2 (2013), 167–199  crossref  isi
    32. Vedenyapin V.V., Negmatov M.A., “O topologii statsionarnykh reshenii gidrodinamicheskikh i vikhrevykh sledstvii uravneniya vlasova i metod gamiltona–yakobi”, Doklady akademii nauk, 449:5 (2013), 521–521  elib
    33. B. G. Konopelchenko, G. Ortenzi, “Cohomological and Poisson structures and integrable hierarchies in tautological subbundles for Birkhoff strata of the Sato Grassmannian”, Theoret. and Math. Phys., 177:2 (2013), 1479–1491  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    34. Bardos C., Besse N., “The Cauchy Problem for the Vlasov-Dirac-Benney Equation and Related Issues in Fluid Mechanics and Semi-Classical Limits”, Kinet. Relat. Mod., 6:4, SI (2013), 893–917  crossref  isi
    35. M. V. Pavlov, D. V. Prokhorov, A. Yu. Vasiliev, A. M. Zaharov, “Löwner evolution and finite-dimensional reductions of integrable systems”, Theoret. and Math. Phys., 181:1 (2014), 1263–1278  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    36. Yu. A. Mëdova, A. A. Chesnokov, “Shear Hele-Shaw flows of a weakly compressible fluid”, J. Appl. Industr. Math., 9:1 (2015), 88–97  mathnet  crossref  mathscinet
    37. Pavlov M.V., “Hamiltonian Formalism of Two-Dimensional Vlasov Kinetic Equation”, Proc. R. Soc. A-Math. Phys. Eng. Sci., 470:2172 (2014), 20140343  crossref  isi
    38. P. V. Kovtunenko, “Propagation of perturbations in a thin layer of a fluid with viscosity stratification”, J. Math. Sci., 215:4 (2016), 499–509  mathnet  crossref  crossref
    39. Kodama Y. Konopelchenko B. Schief W.K., “Critical Points, Lauricella Functions and Whitham-Type Equations”, J. Phys. A-Math. Theor., 48:22 (2015), 225202  crossref  isi
    40. Y. Kodama, B. G. Konopelchenko, “Confluence of hypergeometric functions and integrable hydrodynamic-type systems”, Theoret. and Math. Phys., 188:3 (2016), 1334–1357  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
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    42. Z. V. Makridin, “An effective algorithm for finding multidimensional conservation laws for integrable systems of hydrodynamic type”, Theoret. and Math. Phys., 194:2 (2018), 274–283  mathnet  crossref  crossref  adsnasa  isi  elib
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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