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Funktsional. Anal. i Prilozhen., 1988, Volume 22, Issue 3, Pages 37–52 (Mi faa1129)  

This article is cited in 63 scientific papers (total in 63 papers)

Method of averaging for two-dimensional “integrable” equations

I. M. Krichever


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English version:
Functional Analysis and Its Applications, 1988, 22:3, 200–213

Bibliographic databases:

UDC: 517.93
Received: 13.10.1986

Citation: I. M. Krichever, “Method of averaging for two-dimensional “integrable” equations”, Funktsional. Anal. i Prilozhen., 22:3 (1988), 37–52; Funct. Anal. Appl., 22:3 (1988), 200–213

Citation in format AMSBIB
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\by I.~M.~Krichever
\paper Method of averaging for two-dimensional ``integrable'' equations
\jour Funktsional. Anal. i Prilozhen.
\yr 1988
\vol 22
\issue 3
\pages 37--52
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\transl
\jour Funct. Anal. Appl.
\yr 1988
\vol 22
\issue 3
\pages 200--213
\crossref{https://doi.org/10.1007/BF01077626}
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    This publication is cited in the following articles:
    1. G. V. Potëmin, “Algebro-geometric construction of self-similar solutions of the Whitham equations”, Russian Math. Surveys, 43:5 (1988), 252–253  mathnet  crossref  mathscinet  adsnasa  isi
    2. 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
    3. 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
    4. V. L. Vereshchagin, “Asymptotic integration of Volterra chains”, Russian Math. Surveys, 45:3 (1990), 226–228  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. 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
    6. B. A. Dubrovin, “Differential geometry of strongly integrable systems of hydrodynamic type”, Funct. Anal. Appl., 24:4 (1990), 280–285  mathnet  crossref  mathscinet  zmath  isi
    7. S. P. Novikov, “Quantization of finite-gap potentials and nonlinear quasiclassical approximation in nonperturbative string theory”, Funct. Anal. Appl., 24:4 (1990), 296–306  mathnet  crossref  mathscinet  zmath  isi
    8. V. R. Kudashev, S. E. Sharapov, “Generalized hodograph method from the group-theoretical point of view”, Theoret. and Math. Phys., 85:2 (1990), 1155–1159  mathnet  crossref  mathscinet  zmath  isi
    9. 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
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    12. A. Ya. Maltsev, M. V. Pavlov, “On Whitham's Averaging Method”, Funct. Anal. Appl., 29:1 (1995), 6–19  mathnet  crossref  mathscinet  zmath  isi
    13. R. F. Bikbaev, “Complex Whitham deformations in the problems with “integrable instability””, Theoret. and Math. Phys., 104:3 (1995), 1078–1097  mathnet  crossref  mathscinet  zmath  isi
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    15. 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
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    18. L. A. Kalyakin, V. A. Lazarev, “Perturbation of the two-soliton solution of the KdV equation”, Theoret. and Math. Phys., 112:1 (1997), 866–874  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    19. A. Ya. Maltsev, “Conservation of Hamiltonian structures in Whitham's averaging method”, Izv. Math., 63:6 (1999), 1171–1201  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    20. A. V. Marshakov, “Strings, SUSY gauge theories, and integrable systems”, Theoret. and Math. Phys., 121:2 (1999), 1409–1461  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    21. 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
    22. D. A. Korotkin, V. B. Matveev, “Theta Function Solutions of the Schlesinger System and the Ernst Equation”, Funct. Anal. Appl., 34:4 (2000), 252–264  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    23. A. V. Zabrodin, “Dispersionless Limit of Hirota Equations in Some Problems of Complex Analysis”, Theoret. and Math. Phys., 129:2 (2001), 1511–1525  mathnet  crossref  crossref  mathscinet  zmath  isi
    24. 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
    25. I. M. Krichever, “Isomonodromy equations on algebraic curves, canonical transformations and Whitham equations”, Mosc. Math. J., 2:4 (2002), 717–752  mathnet  mathscinet  zmath  elib
    26. Klein, C, “Ernst equation, Fay identities and variational formulas on hyperelliptic curves”, Mathematical Research Letters, 9:1 (2002), 27  isi
    27. 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
    28. 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
    29. G. A. El, “The Infinite-Genus Limit of the Whitham Equations”, Theoret. and Math. Phys., 137:2 (2003), 1505–1514  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    30. 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
    31. O. M. Kiselev, “Asymptotics of solutions of higher-dimensional integrable equations and their perturbations”, Journal of Mathematical Sciences, 138:6 (2006), 6067–6230  mathnet  crossref  mathscinet  zmath  elib
    32. Grava T, “Whitham equations, Bergman kernel and Lax-Levermore minimizer”, Acta Applicandae Mathematicae, 82:1 (2004), 1–86  crossref  mathscinet  zmath  isi
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    34. Y. Kodama, B. G. Konopelchenko, L. Martínez Alonso, “Integrable Deformations of Algebraic Curves”, Theoret. and Math. Phys., 144:1 (2005), 961–967  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    35. E. D. Belokolos, V. Z. Ènol'skii, M. Salerno, “Wannier Functions for Quasiperiodic Finite-Gap Potentials”, Theoret. and Math. Phys., 144:2 (2005), 1081–1099  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    36. Abenda, S, “Modulation of Camassa-Holm equation and reciprocal transformations”, Annales de l Institut Fourier, 55:6 (2005), 1803  isi
    37. M. V. Pavlov, “Transformations of integrable hydrodynamic chains and their hydrodynamic reductions”, J. Math. Sci., 151:4 (2008), 3185–3191  mathnet  crossref  mathscinet  zmath  elib  elib
    38. Pavlov, MV, “The Kupershmidt hydrodynamic chains and lattices”, International Mathematics Research Notices, 2006, 46987  isi
    39. Ferapontov, EV, “The Haantjes tensor and double waves for multi-dimensional systems of hydrodynamic type: a necessary condition for integrability”, Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences, 462:2068 (2006), 1197  crossref  isi
    40. Dubrovin, B, “On Hamiltonian perturbations of hyperbolic systems of conservation laws I: Quasi-triviality of bi-Hamiltonian perturbations”, Communications on Pure and Applied Mathematics, 59:4 (2006), 559  crossref  isi
    41. 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
    42. B. G. Konopelchenko, L. Martínez Alonso, E. Medina, “Integrable semiclassical deformations of general algebraic curves and associated conservation laws”, Theoret. and Math. Phys., 151:3 (2007), 820–830  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    43. Abenda, S, “Reciprocal transformations and flat metrics on Hurwitz spaces”, Journal of Physics A-Mathematical and Theoretical, 40:35 (2007), 10769  crossref  isi
    44. Pavlov, MV, “Algebro-geometric approach in the theory of integrable hydrodynamic type systems”, Communications in Mathematical Physics, 272:2 (2007), 469  crossref  isi
    45. A. Ya. Maltsev, “The Lorentz-Invariant Deformation of the Whitham System for the Nonlinear Klein–Gordon Equation”, Funct. Anal. Appl., 42:2 (2008), 103–115  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    46. A. V. Odesskii, V. V. Sokolov, “On (2+1)-Dimensional Hydrodynamic Type Systems Possessing a Pseudopotential with Movable Singularities”, Funct. Anal. Appl., 42:3 (2008), 205–212  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
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    48. S. Yu. Dobrokhotov, D. S. Minenkov, “Remark on the phase shift in the Kuzmak–Whitham ansatz”, Theoret. and Math. Phys., 166:3 (2011), 303–316  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    49. El G.A., Kamchatnov A.M., Pavlov M.V., Zykov S.A., “Kinetic Equation for a Soliton Gas and Its Hydrodynamic Reductions”, J Nonlinear Sci, 21:2 (2011), 151–191  crossref  isi
    50. I. M. Krichever, “Real Normalized Differentials and Arbarello's Conjecture”, Funct. Anal. Appl., 46:2 (2012), 110–120  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    51. Andrei Ya. Maltsev, “Whitham's Method and Dubrovin–Novikov Bracket in Single-Phase and Multiphase Cases”, SIGMA, 8 (2012), 103, 54 pp.  mathnet  crossref
    52. 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
    53. Maltsev A.Ya., “The Multi-Dimensional Hamiltonian Structures in the Whitham Method”, J. Math. Phys., 54:5 (2013), 053507  crossref  isi
    54. A. M. Levin, M. A. Olshanetsky, A. V. Zotov, “Classification of isomonodromy problems on elliptic curves”, Russian Math. Surveys, 69:1 (2014), 35–118  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
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  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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