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Uspekhi Mat. Nauk, 2010, Volume 65, Issue 1(391), Pages 185–186 (Mi umn9342)  

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

In the Moscow Mathematical Society
Communications of the Moscow Mathematical Society

Localized solutions of one-dimensional non-linear shallow-water equations with velocity $c=\sqrt x$

S. Yu. Dobrokhotova, B. Tirozzib

a A. Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences
b University of Rome "La Sapienza"


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English version:
Russian Mathematical Surveys, 2010, 65:1, 177–179

Bibliographic databases:

MSC: 35Q35, 76B15
Presented: И. М. Кричевер
Accepted: 18.12.2009

Citation: S. Yu. Dobrokhotov, B. Tirozzi, “Localized solutions of one-dimensional non-linear shallow-water equations with velocity $c=\sqrt x$”, Uspekhi Mat. Nauk, 65:1(391) (2010), 185–186; Russian Math. Surveys, 65:1 (2010), 177–179

Citation in format AMSBIB
\by S.~Yu.~Dobrokhotov, B.~Tirozzi
\paper Localized solutions of one-dimensional non-linear shallow-water equations with velocity $c=\sqrt x$
\jour Uspekhi Mat. Nauk
\yr 2010
\vol 65
\issue 1(391)
\pages 185--186
\jour Russian Math. Surveys
\yr 2010
\vol 65
\issue 1
\pages 177--179

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    This publication is cited in the following articles:
    1. S. Yu. Dobrokhotov, V. E. Nazaǐkinskiǐ, B. Tirozzi, “Asymptotic solutions of the two-dimensional model wave equation with degenerating velocity and localized initial data”, St. Petersburg Math. J., 22:6 (2011), 895–911  mathnet  crossref  mathscinet  zmath  isi
    2. Dobrokhotov S.Yu., Nazaikinskii V.E., Tirozzi B., “Asymptotic solution of the one-dimensional wave equation with localized initial data and with degenerating velocity. I”, Russ. J. Math. Phys., 17:4 (2010), 434–447  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. V. E. Nazaikinskii, “Degenerate Wave Equation with Localized Initial Data: Asymptotic Solutions Corresponding to Various Self-Adjoint Extensions”, Math. Notes, 89:5 (2011), 749–753  mathnet  crossref  crossref  mathscinet  isi
    4. Choi B.H., Kaistrenko V., Kim K.O., Min B.I., Pelinovsky E., “Rapid forecasting of tsunami runup heights from 2-D numerical simulations”, Natural Hazards and Earth System Sciences, 11:3 (2011), 707–714  crossref  adsnasa  isi
    5. Didenkulova I., Pelinovsky E., “Nonlinear wave evolution and runup in an inclined channel of a parabolic cross-section”, Phys. Fluids, 23:8 (2011), 086602, 15 pp.  crossref  adsnasa  isi  elib
    6. V. E. Nazaikinskii, “Phase Space Geometry for a Wave Equation Degenerating on the Boundary of the Domain”, Math. Notes, 92:1 (2012), 144–148  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    7. D. S. Minenkov, “Asymptotics of the Solutions of the One-Dimensional Nonlinear System of Equations of Shallow Water with Degenerate Velocity”, Math. Notes, 92:5 (2012), 664–672  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    8. S. Yu. Dobrokhotov, S. B. Medvedev, D. S. Minenkov, “On Replacements Reducing One-Dimensional Systems of Shallow-Water Equations to the Wave Equation with Sound Speed $c^2=x$”, Math. Notes, 93:5 (2013), 704–714  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    9. Pelinovsky E.N., Rodin A.A., “Nonlinear Effects at the Initial Stage of Tsunami-Wave Development”, Izv. Atmos. Ocean. Phys., 49:5 (2013), 548–553  crossref  mathscinet  isi
    10. Ezersky A., Tiguercha D., Pelinovsky E., “Resonance Phenomena at the Long Wave Run-Up on the Coast”, Nat. Hazards Earth Syst. Sci., 13:11 (2013), 2745–2752  crossref  adsnasa  isi
    11. Dobrokhotov S.Yu., Nazaikinskii V.E., Tirozzi B., “Two-Dimensional Wave Equation with Degeneration on the Curvilinear Boundary of the Domain and Asymptotic Solutions with Localized Initial Data”, Russ. J. Math. Phys., 20:4 (2013), 389–401  crossref  mathscinet  zmath  isi
    12. Yu. A. Chirkunov, S. Yu. Dobrokhotov, S. B. Medvedev, D. S. Minenkov, “Exact solutions of one-dimensional nonlinear shallow water equations over even and sloping bottoms”, Theoret. and Math. Phys., 178:3 (2014), 278–298  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    13. V. E. Nazaikinskii, “The Maslov Canonical Operator on Lagrangian Manifolds in the Phase Space Corresponding to a Wave Equation Degenerating on the Boundary”, Math. Notes, 96:2 (2014), 248–260  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    14. I. I. Didenkulova, E. N. Pelinovskii, O. I. Didenkulov, “Nakat dlinnykh uedinennykh voln razlichnoi polyarnosti na ploskii otkos”, Izv. RAN. Fizika atmosfery i okeana, 50:5 (2014), 604–611  crossref  mathscinet  elib
    15. Didenkulova I.I., Pelinovsky E.N., Didenkulov O.I., “Run-Up of Long Solitary Waves of Different Polarities on a Plane Beach”, Izv. Atmos. Ocean. Phys., 50:5 (2014), 532–538  crossref  isi
    16. Rybkin A., Pelinovsky E., Didenkulova I., “Nonlinear Wave Run-Up in Bays of Arbitrary Cross-Section: Generalization of the Carrier-Greenspan Approach”, J. Fluid Mech., 748 (2014), 416–432  crossref  mathscinet  isi
    17. Nazaikinskii V.E., “Maslov's Canonical Operator For Degenerate Hyperbolic Equations”, Russ. J. Math. Phys., 21:2 (2014), 289–290  crossref  mathscinet  zmath  isi
    18. Didenkulov O.I., Didenkulova I.I., Pelinovsky E.N., Kurkin A.A., “Influence of the Shape of the Bay Cross Section on Wave Run-Up”, 51, no. 6, 2015, 661–666  crossref  isi
    19. Dynnikov I.A., Mironov A.E., Taimanov I.A., Vesnin A.Yu., “The Conference ‘’Dynamics in Siberia", Novosibirsk, February 29 - March 4, 2016”, Sib. Electron. Math. Rep., 13 (2016), A1–A41  mathnet  crossref  mathscinet  isi
    20. An. G. Marchuk, “The assessment of tsunami heights above the parabolic bottom relief within the wave-ray approach”, Num. Anal. Appl., 10:1 (2017), 17–27  mathnet  crossref  crossref  mathscinet  isi  elib
    21. Lozhnikov D.A., Nazaikinskii V.E., “Method For the Analysis of Long Water Waves Taking Into Account Reflection From a Gently Sloping Beach”, Pmm-J. Appl. Math. Mech., 81:1 (2017), 21–28  crossref  mathscinet  isi
    22. Minenkov D.S., “Asymptotics Near the Shore For 2D Shallow Water Over Sloping Planar Bottom”, Proceedings of the International Conference Days on Diffraction (Dd) 2017, eds. Motygin O., Kiselev A., Goray L., Suslina T., Kazakov A., Kirpichnikova A., IEEE, 2017, 240–243  isi
    23. A. V. Aksenov, S. Yu. Dobrokhotov, K. P. Druzhkov, “Exact Step-Like Solutions of One-Dimensional Shallow-Water Equations over a Sloping Bottom”, Math. Notes, 104:6 (2018), 915–921  mathnet  crossref  crossref  isi  elib
    24. Pelinovsky E., Talipova T., Didenkulova I., Didenkulova (Shurgalina) Ekaterina, “Interfacial Long Traveling Waves in a Two-Layer Fluid With Variable Depth”, Stud. Appl. Math., 142:4, SI (2019), 513–527  crossref  isi  scopus
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