L. Martínez Alonso, A. B. Shabat, “Hydrodynamic Reductions and Solutions of a Universal Hierarchy”, TMF, 140:2 (2004), 216–229; Theoret. and Math. Phys., 140:2 (2004), 1073

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Teoreticheskaya i Matematicheskaya Fizika, 2004, Volume 140, Number 2, Pages 216–229
DOI: https://doi.org/10.4213/tmf91 (Mi tmf91)

This article is cited in 85 scientific papers (total in 85 papers)

Hydrodynamic Reductions and Solutions of a Universal Hierarchy

L. Martínez Alonso^a, A. B. Shabat^b

^a Universidad Complutense, Departamento de Fisica Teorica II
^b L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences

Full-text PDF (258 kB) Citations (85)

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DOI: https://doi.org/10.4213/tmf91

Abstract: We investigate the diagonal hydrodynamic reductions of a hierarchy of integrable hydrodynamic chains and analyze their compatibility with previously introduced reductions of differential type.

Keywords: hydrodynamic systems, differential reductions, hodograph solutions.

Received: 17.09.2003

English version:
Theoretical and Mathematical Physics, 2004, Volume 140, Issue 2, Pages 1073–1085
DOI: https://doi.org/10.1023/B:TAMP.0000036538.41884.57

Bibliographic databases:

Language: Russian

Citation: L. Martínez Alonso, A. B. Shabat, “Hydrodynamic Reductions and Solutions of a Universal Hierarchy”, TMF, 140:2 (2004), 216–229; Theoret. and Math. Phys., 140:2 (2004), 1073–1085

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tmf91

https://doi.org/10.4213/tmf91

https://www.mathnet.ru/eng/tmf/v140/i2/p216

This publication is cited in the following 85 articles:

E. V. Ferapontov, V. S. Novikov, I. Roustemoglou, “Higher-order reductions of the Mikhalev system”, Lett Math Phys, 114:3 (2024)
Naseem Abbas, Akhtar Hussain, Muhammad Waseem Akram, Shah Muhammad, Mohammad Shuaib, “Invariant analysis of the multidimensional Martinez Alonso–Shabat equation”, Zeitschrift für Naturforschung A, 2024
V. E. Adler, “3D consistency of negative flows”, Theoret. and Math. Phys., 221:2 (2024), 1836–1851
O. E. Hentosh, Ya.A. Prykarpatskyy, A. A. Balinsky, A. K. Prykarpatski, “Geometric Structures on the Orbits of Loop Diffeomorphism Groups and Related Heavenly-Type Hamiltonian Systems. II”, Ukr Math J, 74:9 (2023), 1348
Petr Vojčák, “Non-Abelian covering and new recursion operators for the 4D Martínez Alonso–Shabat equation”, Communications in Nonlinear Science and Numerical Simulation, 118 (2023), 107007
O. E. Hentosh, Ya.A. Prykarpatskyy, A. A. Balinsky, A. K. Prykarpatski, “Geometric Structures on the Orbits of Loop Diffeomorphism Groups and Related Heavenly-Type Hamiltonian Systems. I”, Ukr Math J, 74:8 (2023), 1175
I. S. Krasil'shchik, O. I. Morozov, “Lagrangian extensions of multi-dimensional integrable equations. I. The five-dimensional Martínez Alonso–Shabat equation”, Anal.Math.Phys., 13:1 (2023)
Krasil'shchik I.S., Verbovetsky A.M., “Recursion Operators in the Cotangent Covering of the Rddym Equation”, Anal. Math. Phys., 12:1 (2022), 1
Makridin V Z. Pavlov V M., “Multidimensional Conservation Laws and Integrable Systems II”, Stud. Appl. Math., 148:2 (2022), 813–824
Bilal M., Ur-Rehman Sh., Ahmad J., “Lump-Periodic, Some Interaction Phenomena and Breather Wave Solutions to the (2+1)-Rth Dispersionless Dym Equation”, Mod. Phys. Lett. B, 36:02 (2022), 2150547
O. E. Hentosh, Ya. A. Prykarpatskyy, A. A. Balinsky, A. K. Prykarpatski, “Geometrichnі strukturi na orbіtakh petelnikh grup difeomorfіzmіv ta asotsіiovanі іntegrovnі gamіltonovі sistemi „nebesnogo" tipu. II”, Ukr. Mat. Zhurn., 74:9 (2022), 1182
O. I. Morozov, “Integrability Properties of the Four-Dimensional Equation of Universal Hierarchy”, J Math Sci, 263:3 (2022), 396
Anatolij K. Prykarpatski, “Quantum Current Algebra in Action: Linearization, Integrability of Classical and Factorization of Quantum Nonlinear Dynamical Systems”, Universe, 8:5 (2022), 288
O. I. Morozov, “Higher Symmetries of the Cotangent Covering for the Modified Veronese Web Equation”, Lobachevskii J Math, 43:10 (2022), 2797
Abdullahi Yusuf, Ali S. Alshomrani, Tukur Abdulkadir Sulaiman, Usman Younas, Dumitru Baleanu, “On the breather waves, lump solutions, two-wave solutions of (3+1) dimensional Martínez Alonso–Shabat equation”, Journal of Ocean Engineering and Science, 2022
M. M. Prytula, “New Completely Integrable Dispersionless Dynamical System of Heavenly Type Generated By Vector Fields on a Torus”, J Math Sci, 265:4 (2022), 682
Jan L. Cieśliński, Dzianis Zhalukevich, “Spectral Parameter as a Group Parameter”, Symmetry, 14:12 (2022), 2577
Usman Younas, T.A. Sulaiman, Jingli Ren, A. Yusuf, “Lump interaction phenomena to the nonlinear ill-posed Boussinesq dynamical wave equation”, Journal of Geometry and Physics, 178 (2022), 104586
Krasil'shchik I.S., Vojcak P., “On the Algebra of Nonlocal Symmetries For the 4D Martinez Alonso-Shabat Equation”, J. Geom. Phys., 163 (2021), 104122
Morozov I O., “Isospectral Deformation of the Reduced Quasi-Classical Self-Dual Yang?Mills Equation”, Differ. Geom. Appl., 76 (2021), 101742

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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