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Russian Mathematical Surveys, 1989, Volume 44, Issue 6, Pages 35–124
DOI: https://doi.org/10.1070/RM1989v044n06ABEH002300
(Mi rm1948)
 

This article is cited in 318 scientific papers (total in 319 papers)

Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory

B. A. Dubrovin, S. P. Novikov
References:
Received: 12.07.1989
Bibliographic databases:
Document Type: Article
UDC: 514.8
Language: English
Original paper language: Russian
Citation: 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
Citation in format AMSBIB
\Bibitem{DubNov89}
\by B.~A.~Dubrovin, S.~P.~Novikov
\paper Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory
\jour Russian Math. Surveys
\yr 1989
\vol 44
\issue 6
\pages 35--124
\mathnet{http://mi.mathnet.ru/eng/rm1948}
\crossref{https://doi.org/10.1070/RM1989v044n06ABEH002300}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1037010}
\zmath{https://zbmath.org/?q=an:0712.58032}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?1989RuMaS..44...35D}
Linking options:
  • https://www.mathnet.ru/eng/rm1948
  • https://doi.org/10.1070/RM1989v044n06ABEH002300
  • https://www.mathnet.ru/eng/rm/v44/i6/p29
    Erratum
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    2. Thibault Bonnemain, Vincent Caudrelier, Benjamin Doyon, “Hamiltonian Formulation and Aspects of Integrability of Generalised Hydrodynamics”, Ann. Henri Poincaré, 2025  crossref
    3. Nan-Nan Wei, Hai-Qiang Zhang, Dong-Rao Jing, Xin-Kai Chu, “Rarefaction waves and dispersive shock waves in fluid dynamics to the higher-order Gerdjikov–Ivanov model”, Physics of Fluids, 37:3 (2025)  crossref
    4. Haili Li, Deng-Shan Wang, “Wave motions in discontinuous initial-value problem of the inviscid shallow water wave Jaulent-Miodek model”, DCDS-B, 2024  crossref
    5. Jing Chen, Ao Zhou, Yushan Xue, “Evolution of initial discontinuities in a particular case of two-step initial problem for the defocusing complex modified KdV equation”, Journal of Mathematical Analysis and Applications, 536:2 (2024), 128227  crossref
    6. Sergei Agapov, Vladislav Shubin, “New examples of non-polynomial integrals of two-dimensional geodesic flows *”, J. Phys. A: Math. Theor., 57:1 (2024), 015204  crossref
    7. Gino Biondini, Alexander J Bivolcic, Mark A Hoefer, Antonio Moro, “Two-dimensional reductions of the Whitham modulation system for the Kadomtsev–Petviashvili equation”, Nonlinearity, 37:2 (2024), 025012  crossref
    8. Alfred Michel Grundland, “On k-wave solutions of quasilinear systems of partial differential equations”, Open Communications in Nonlinear Mathematical Physics, Special Issue in Memory of... (2024)  crossref
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    10. M. V. Pavlov, “Compatible Pairs of Dubrovin–Novikov Poisson Brackets and Lagrangian Representations of Integrable Hierarchies”, Proc. Steklov Inst. Math., 325 (2024), 224–229  mathnet  crossref  crossref  zmath
    11. Zhi‐Jia Wu, Shou‐Fu Tian, “Whitham modulation theory and the classification of solutions to the Riemann problem of the Fokas–Lenells equation”, Stud Appl Math, 2024  crossref
    12. T. Congy, G. A. El, G. Roberti, A. Tovbis, “Dispersive Hydrodynamics of Soliton Condensates for the Korteweg–de Vries Equation”, J Nonlinear Sci, 33:6 (2023)  crossref
    13. A. M. Kamchatnov, “Evolution of Nonlinear Wave Pulses in the sine-Gordon Equation Theory”, J. Exp. Theor. Phys., 136:5 (2023), 653  crossref
    14. Alexey V. Bolsinov, Andrey Yu. Konyaev, Vladimir S. Matveev, “Applications of Nijenhuis Geometry III: Frobenius Pencils and Compatible Non-homogeneous Poisson Structures”, J Geom Anal, 33:6 (2023)  crossref
    15. R Camassa, G Falqui, G Ortenzi, M Pedroni, T T Vu Ho, “Simple two-layer dispersive models in the Hamiltonian reduction formalism”, Nonlinearity, 36:9 (2023), 4523  crossref
    16. Huan Gao, Deng-Shan Wang, “Optical undular bores in Riemann problem of photon fluid with quintic nonlinearity”, Phys. Rev. E, 108:2 (2023)  crossref
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    18. Deng-Shan Wang, Ling Xu, Zuxing Xuan, “The Complete Classification of Solutions to the Riemann Problem of the Defocusing Complex Modified KdV Equation”, J Nonlinear Sci, 32:1 (2022)  crossref
    19. E.V. Ferapontov, M. V. Pavlov, “Kinetic Equation for Soliton Gas: Integrable Reductions”, J Nonlinear Sci, 32:2 (2022)  crossref
    20. A. V. Domrin, M. A. Shumkin, B. I. Suleimanov, “Meromorphy of solutions for a wide class of ordinary differential equations of Painlevé type”, Journal of Mathematical Physics, 63:2 (2022)  crossref
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    References:175
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