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Volumn 44, Issue 9, 2003, Pages 4134-4156

Integrable hydrodynamic chains

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EID: 0242473122     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1597946     Document Type: Article
Times cited : (169)

References (49)
  • 1
    • 0035778223 scopus 로고    scopus 로고
    • Symmetries and relations between solutions of a class of Euler-Poisson-Darboux equations
    • Aksenov, A. V., "Symmetries and relations between solutions of a class of Euler-Poisson-Darboux equations," Dokl. Akad. Nauk 381, 176-179 (2001).
    • (2001) Dokl. Akad. Nauk , vol.381 , pp. 176-179
    • Aksenov, A.V.1
  • 2
    • 0000893285 scopus 로고
    • Associated integrable systems
    • Alber, S. J., "Associated integrable systems," J. Math. Phys. 32, 916-922 (1991).
    • (1991) J. Math. Phys. , vol.32 , pp. 916-922
    • Alber, S.J.1
  • 3
    • 0038861891 scopus 로고    scopus 로고
    • The symmetry structure of the heavenly equation
    • Alfinito, E., Soliani, G., and Solombrino, L., "The symmetry structure of the heavenly equation," Lett. Math. Phys. 41, 379-389 (1997).
    • (1997) Lett. Math. Phys. , vol.41 , pp. 379-389
    • Alfinito, E.1    Soliani, G.2    Solombrino, L.3
  • 4
    • 0037043282 scopus 로고    scopus 로고
    • Energy-dependent potentials revisited: A universal hierarchy of hydrodynamic type
    • Alonso, L. M. and Shabat, A. B., "Energy-dependent potentials revisited: A universal hierarchy of hydrodynamic type," Phys. Lett. A 299, 359-365 (2002).
    • (2002) Phys. Lett. A , vol.299 , pp. 359-365
    • Alonso, L.M.1    Shabat, A.B.2
  • 5
    • 0015604573 scopus 로고
    • Some properties of long non-linear waves
    • Benney, D. J., "Some properties of long non-linear waves," Stud. Appl. Math. 52, 45-50 (1973).
    • (1973) Stud. Appl. Math. , vol.52 , pp. 45-50
    • Benney, D.J.1
  • 6
    • 0037032762 scopus 로고    scopus 로고
    • Classical R-matrix theory of dispersionless systems: I. (1 + 1) -dimension theory
    • Blaszak, M. and Szablikowski, B. M., "Classical R-matrix theory of dispersionless systems: I. (1 + 1)-dimension theory," J. Phys. A 35, 10325-10344 (2002); "Classical R-matrix theory of dispersionless systems: II. (2 + 1)-dimension theory," ibid. 35, 10345-10364 (2002).
    • (2002) J. Phys. A , vol.35 , pp. 10325-10344
    • Blaszak, M.1    Szablikowski, B.M.2
  • 7
    • 0042882776 scopus 로고    scopus 로고
    • Classical R-matrix theory of dispersionless systems: II. (2 + 1)-dimension theory
    • Blaszak, M. and Szablikowski, B. M., "Classical R-matrix theory of dispersionless systems: I. (1 + 1)-dimension theory," J. Phys. A 35, 10325-10344 (2002); "Classical R-matrix theory of dispersionless systems: II. (2 + 1)-dimension theory," ibid. 35, 10345-10364 (2002).
    • (2002) J. Phys. A , vol.35 , pp. 10345-10364
  • 9
    • 0011401791 scopus 로고
    • Hamiltonian formalism of Whitham-type hierarchies and topological Landau-Ginsburg models
    • Dubrovin, B. A., "Hamiltonian formalism of Whitham-type hierarchies and topological Landau-Ginsburg models," Commun. Math. Phys. 145, 195-207 (1992).
    • (1992) Commun. Math. Phys. , vol.145 , pp. 195-207
    • Dubrovin, B.A.1
  • 10
    • 0001392731 scopus 로고
    • Hamiltonian formalism of one-dimensional systems of hydrodynamic type and the Bogolyubov-Whitham averaging method
    • Dubrovin, B. A. and Novikov, S. P., "Hamiltonian formalism of one-dimensional systems of hydrodynamic type and the Bogolyubov-Whitham averaging method," Sov. Math. Dokl. 27, 665-669 (1983); "Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory," Russ. Math. Surveys 44, 35-124 (1989).
    • (1983) Sov. Math. Dokl. , vol.27 , pp. 665-669
    • Dubrovin, B.A.1    Novikov, S.P.2
  • 11
    • 0347767249 scopus 로고
    • Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory
    • Dubrovin, B. A. and Novikov, S. P., "Hamiltonian formalism of one-dimensional systems of hydrodynamic type and the Bogolyubov-Whitham averaging method," Sov. Math. Dokl. 27, 665-669 (1983); "Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory," Russ. Math. Surveys 44, 35-124 (1989).
    • (1989) Russ. Math. Surveys , vol.44 , pp. 35-124
  • 12
    • 0003431721 scopus 로고
    • Princeton University Press, Princeton, NJ; 2nd ed. (Chelsea, New York)
    • Eisenhart, L. P., Transformations of surfaces (Princeton University Press, Princeton, NJ, 1923); 2nd ed. (Chelsea, New York, 1962); Gronwall, T. H., "Tri-ortogonal curvilinear coordinate systems and generalization of Euler-Darboux-Poisson equation," Ann. Math. 20, 262-263 (1918/19).
    • (1923) Transformations of Surfaces
    • Eisenhart, L.P.1
  • 13
    • 0242609527 scopus 로고
    • Tri-ortogonal curvilinear coordinate systems and generalization of Euler-Darboux-Poisson equation
    • Eisenhart, L. P., Transformations of surfaces (Princeton University Press, Princeton, NJ, 1923); 2nd ed. (Chelsea, New York, 1962); Gronwall, T. H., "Tri-ortogonal curvilinear coordinate systems and generalization of Euler-Darboux-Poisson equation," Ann. Math. 20, 262-263 (1918/19).
    • (1918) Ann. Math. , vol.20 , pp. 262-263
    • Gronwall, T.H.1
  • 14
    • 0001247522 scopus 로고
    • Integration of weakly nonlinear hydrodynamic systems in Riemann invariants
    • Ferapontov, E. V., "Integration of weakly nonlinear hydrodynamic systems in Riemann invariants," Phys. Lett. A 158, 112-118 (1991).
    • (1991) Phys. Lett. A , vol.158 , pp. 112-118
    • Ferapontov, E.V.1
  • 15
    • 0042746739 scopus 로고
    • Hamiltonian systems of hydrodynamic type and their realization on hypersurfaces of pseudo-Euclidean space
    • Ferapontov, E. V., "Hamiltonian systems of hydrodynamic type and their realization on hypersurfaces of pseudo-Euclidean space," J. Sov. Math. 55, 1970-1995 (1991).
    • (1991) J. Sov. Math. , vol.55 , pp. 1970-1995
    • Ferapontov, E.V.1
  • 16
    • 0001833648 scopus 로고
    • Nonlocal Hamiltonian operators of hydrodynamic type: Differential geometry and applications
    • Ferapontov, E. V., "Nonlocal Hamiltonian operators of hydrodynamic type: differential geometry and applications," Am. Math. Soc. Trans. 170, 33-58 (1995).
    • (1995) Am. Math. Soc. Trans. , vol.170 , pp. 33-58
    • Ferapontov, E.V.1
  • 17
    • 0031558537 scopus 로고    scopus 로고
    • Laplace transformations of hydrodynamic type systems in Riemann invariants: Periodic sequences
    • Ferapontov, E. V., "Laplace transformations of hydrodynamic type systems in Riemann invariants: periodic sequences," J. Phys. A 30, 6861-6878 (1997).
    • (1997) J. Phys. A , vol.30 , pp. 6861-6878
    • Ferapontov, E.V.1
  • 19
    • 0002379586 scopus 로고
    • Quasiclassical limit of coupled KdV equations, Riemann invariants and multi-Hamiltonian structure
    • Ferapontov, E. V. and Pavlov, M. V., "Quasiclassical limit of coupled KdV equations, Riemann invariants and multi-Hamiltonian structure, " Physica D 52, 211-219 (1991).
    • (1991) Physica D , vol.52 , pp. 211-219
    • Ferapontov, E.V.1    Pavlov, M.V.2
  • 20
    • 0037364754 scopus 로고    scopus 로고
    • Reciprocal transformations of Hamiltonian operators of hydrodynamic type: Nonlocal Hamiltonian formalism for linearly degenerate systems
    • Ferapontov, E. V. and Pavlov, M. V., "Reciprocal transformations of Hamiltonian operators of hydrodynamic type: nonlocal Hamiltonian formalism for linearly degenerate systems," J. Math. Phys. 44, 1150-1172 (2003).
    • (2003) J. Math. Phys. , vol.44 , pp. 1150-1172
    • Ferapontov, E.V.1    Pavlov, M.V.2
  • 21
    • 0037534179 scopus 로고    scopus 로고
    • Hydrodynamic reductions of the heavenly equation
    • Ferapontov, E. V. and Pavlov, M. V., "Hydrodynamic reductions of the heavenly equation," Class. Quantum Grav. 20, 2429-2441 (2003).
    • (2003) Class. Quantum Grav. , vol.20 , pp. 2429-2441
    • Ferapontov, E.V.1    Pavlov, M.V.2
  • 22
    • 4244024077 scopus 로고
    • On the continuous Benney equations
    • Geogjaev, V. V., "On the continuous Benney equations," Physica D 87, 168-175 (1995).
    • (1995) Physica D , vol.87 , pp. 168-175
    • Geogjaev, V.V.1
  • 23
    • 0000006540 scopus 로고
    • Collisionless Boltzmann equations and integrable moment equations
    • Gibbons, J., "Collisionless Boltzmann equations and integrable moment equations," Physica D 3, 503-511 (1981).
    • (1981) Physica D , vol.3 , pp. 503-511
    • Gibbons, J.1
  • 24
    • 0002714967 scopus 로고    scopus 로고
    • Reductions of Benney's equations
    • Gibbons, J. and Tsarev, S. P., "Reductions of Benney's equations," Phys. Lett. A 211, 19-24 (1996); "Conformal maps and reductions of the Benney equations," ibid. 258, 263-270 (1999).
    • (1996) Phys. Lett. A , vol.211 , pp. 19-24
    • Gibbons, J.1    Tsarev, S.P.2
  • 25
    • 0347245477 scopus 로고    scopus 로고
    • Conformal maps and reductions of the Benney equations
    • Gibbons, J. and Tsarev, S. P., "Reductions of Benney's equations," Phys. Lett. A 211, 19-24 (1996); "Conformal maps and reductions of the Benney equations," ibid. 258, 263-270 (1999).
    • (1999) Phys. Lett. A , vol.258 , pp. 263-270
  • 26
    • 34250384767 scopus 로고
    • Nonlinear evolution equations associated with energy-dependent Schrödinger potentials
    • Jaulent, M. and Miodek, Y., "Nonlinear evolution equations associated with energy-dependent Schrödinger potentials," Lett. Math. Phys. 1, 243-250 (1975/77); Fordy, A. P., "Isospectral flows: their Hamiltonian structures, Miura maps and master symmetries," in Solitons in Physics, Mathematics, and Nonlinear Optics, edited by P. J. Olver and D. L. Sattinger (Springer, New York, 1990), pp. 97-121.
    • (1975) Lett. Math. Phys. , vol.1 , pp. 243-250
    • Jaulent, M.1    Miodek, Y.2
  • 27
    • 0242693631 scopus 로고
    • Isospectral flows: Their Hamiltonian structures, Miura maps and master symmetries
    • edited by P. J. Olver and D. L. Sattinger (Springer, New York)
    • Jaulent, M. and Miodek, Y., "Nonlinear evolution equations associated with energy-dependent Schrödinger potentials," Lett. Math. Phys. 1, 243-250 (1975/77); Fordy, A. P., "Isospectral flows: their Hamiltonian structures, Miura maps and master symmetries," in Solitons in Physics, Mathematics, and Nonlinear Optics, edited by P. J. Olver and D. L. Sattinger (Springer, New York, 1990), pp. 97-121.
    • (1990) Solitons in Physics, Mathematics, and Nonlinear Optics , pp. 97-121
    • Fordy, A.P.1
  • 28
    • 0005135586 scopus 로고
    • Solution of the dispersionless Toda equation
    • Kodama, Y., "Solution of the dispersionless Toda equation," Phys. Lett. A 147, 477-480 (1990); Yu, L., "Waterbag reductions of the dispersionless discrete KP hierarchy," J. Phys. A 33, 8127-8138 (2000).
    • (1990) Phys. Lett. A , vol.147 , pp. 477-480
    • Kodama, Y.1
  • 29
    • 0039606645 scopus 로고    scopus 로고
    • Waterbag reductions of the dispersionless discrete KP hierarchy
    • Kodama, Y., "Solution of the dispersionless Toda equation," Phys. Lett. A 147, 477-480 (1990); Yu, L., "Waterbag reductions of the dispersionless discrete KP hierarchy," J. Phys. A 33, 8127-8138 (2000).
    • (2000) J. Phys. A , vol.33 , pp. 8127-8138
    • Yu, L.1
  • 30
    • 0037512871 scopus 로고
    • The dispersionless Lax equations and topological minimal models
    • Krichever, I. M., "The dispersionless Lax equations and topological minimal models," Commun. Math. Phys. 143, 415-429 (1992); "The τ-function of the universal Whitham hierarchy, matrix models and topological field theories," Commun. Pure Appl. Math. 47, 437-475 (1994).
    • (1992) Commun. Math. Phys. , vol.143 , pp. 415-429
    • Krichever, I.M.1
  • 31
    • 84990709711 scopus 로고
    • The τ-function of the universal Whitham hierarchy, matrix models and topological field theories
    • Krichever, I. M., "The dispersionless Lax equations and topological minimal models," Commun. Math. Phys. 143, 415-429 (1992); "The τ-function of the universal Whitham hierarchy, matrix models and topological field theories," Commun. Pure Appl. Math. 47, 437-475 (1994).
    • (1994) Commun. Pure Appl. Math. , vol.47 , pp. 437-475
  • 32
    • 0009017579 scopus 로고
    • Long wave equations with a free surface. II. The Hamiltonian structure and the higher equations
    • Kupershmidt, B. A. and Manin, Y. I., "Long wave equations with a free surface. II. The Hamiltonian structure and the higher equations," Funct. Anal. Appl. 12, 25-37 (1978).
    • (1978) Funct. Anal. Appl. , vol.12 , pp. 25-37
    • Kupershmidt, B.A.1    Manin, Y.I.2
  • 33
    • 0001338252 scopus 로고
    • Conservation laws and Lax representation of Benney's long wave equations
    • Lebedev, D. R., and Manin, Y. I., "Conservation laws and Lax representation of Benney's long wave equations," Phys. Lett. A 74, 154-156 (1979).
    • (1979) Phys. Lett. A , vol.74 , pp. 154-156
    • Lebedev, D.R.1    Manin, Y.I.2
  • 34
    • 0002431409 scopus 로고
    • Hamiltonian formalism of Korteweg-de Vries-type hierarchies
    • Mikhalev, V. G., "Hamiltonian formalism of Korteweg-de Vries-type hierarchies," Funct. Anal. Appl. 26 (2), 140-142 (1992).
    • (1992) Funct. Anal. Appl. , vol.26 , Issue.2 , pp. 140-142
    • Mikhalev, V.G.1
  • 35
    • 36549092846 scopus 로고
    • On a new class of completely integrable nonlinear wave equations. Multi-Hamiltonian structure II
    • Nutku, Y., "On a new class of completely integrable nonlinear wave equations. Multi-Hamiltonian structure II," J. Math. Phys. 28, 2579-2585 (1987).
    • (1987) J. Math. Phys. , vol.28 , pp. 2579-2585
    • Nutku, Y.1
  • 37
    • 0013039519 scopus 로고
    • Hamiltonian formalism of weakly nonlinear systems in hydrodynamics
    • Pavlov, M. V., "Hamiltonian formalism of weakly nonlinear systems in hydrodynamics," Theor. Math. Phys. 73, 316-320 (1987).
    • (1987) Theor. Math. Phys. , vol.73 , pp. 316-320
    • Pavlov, M.V.1
  • 38
    • 0242609533 scopus 로고
    • Ph.D. Thesis, Landau ITP, Moscow
    • Pavlov, M. V., Ph.D. Thesis, Landau ITP, Moscow, 1992.
    • (1992)
    • Pavlov, M.V.1
  • 39
    • 0040314027 scopus 로고
    • Elliptic coordinates and multi-Hamiltonian structures of hydrodynamic type systems
    • Pavlov, M. V., "Elliptic coordinates and multi-Hamiltonian structures of hydrodynamic type systems," Rep. RAS, 339 (1), 21-23 (1994).
    • (1994) Rep. RAS , vol.339 , Issue.1 , pp. 21-23
    • Pavlov, M.V.1
  • 40
    • 0242609532 scopus 로고
    • Exact integrability of a system of Benney equations
    • Pavlov, M. V., "Exact integrability of a system of Benney equations," Phys. Dokl. 39, 745-747 (1994); "Local Hamiltonian structures of Benney's system;" ibid. 39, 607-608 (1994)
    • (1994) Phys. Dokl. , vol.39 , pp. 745-747
    • Pavlov, M.V.1
  • 41
    • 0040575170 scopus 로고
    • Local Hamiltonian structures of Benney's system
    • Pavlov, M. V., "Exact integrability of a system of Benney equations," Phys. Dokl. 39, 745-747 (1994); "Local Hamiltonian structures of Benney's system;" ibid. 39, 607-608 (1994)
    • (1994) Phys. Dokl. , vol.39 , pp. 607-608
  • 42
    • 0037245698 scopus 로고    scopus 로고
    • Three-Hamiltonian structures of the Egorov hydrodynamic type systems
    • Pavlov, M. V. and Tsarev, S. P., "Three-Hamiltonian structures of the Egorov hydrodynamic type systems," Funct. Anal. Appl. 37, 32-45 (2003).
    • (2003) Funct. Anal. Appl. , vol.37 , pp. 32-45
    • Pavlov, M.V.1    Tsarev, S.P.2
  • 43
    • 0003872030 scopus 로고
    • Systems of quasilinear equations and their applications to gas dynamics
    • translated from the second Russian edition by J. R. Schulenberger, American Mathematical Society, Providence, RI, Russian ed. (Nauka, Moscow)
    • Rozhdestvenski, B. L. and Yanenko, N. N., "Systems of quasilinear equations and their applications to gas dynamics," translated from the second Russian edition by J. R. Schulenberger, Translations of Mathematical Monographs, 55 (American Mathematical Society, Providence, RI, 1983), Russian ed. (Nauka, Moscow, 1968).
    • (1968) Mathematical Monographs , vol.55
    • Rozhdestvenski, B.L.1    Yanenko, N.N.2
  • 44
    • 0000670902 scopus 로고
    • On Poisson brackets and one-dimensional Hamiltonian systems of hydrodynamic type
    • Tsarev, S. P., "On Poisson brackets and one-dimensional Hamiltonian systems of hydrodynamic type," Sov. Math. Dokl. 31, 488-491 (1985); "The geometry Hamiltonian systems of hydrodynamic type. The generalized hodograph method," Math. USSR, Izv. 37, 397-419 (1991).
    • (1985) Sov. Math. Dokl. , vol.31 , pp. 488-491
    • Tsarev, S.P.1
  • 45
    • 33646977967 scopus 로고
    • The geometry Hamiltonian systems of hydrodynamic type. The generalized hodograph method
    • Tsarev, S. P., "On Poisson brackets and one-dimensional Hamiltonian systems of hydrodynamic type," Sov. Math. Dokl. 31, 488-491 (1985); "The geometry Hamiltonian systems of hydrodynamic type. The generalized hodograph method," Math. USSR, Izv. 37, 397-419 (1991).
    • (1991) Math. USSR, Izv. , vol.37 , pp. 397-419
  • 47
    • 0242441213 scopus 로고
    • Integration of chromatography equations for Lengmur isoterm of absorption
    • VNIIFTRI, in Russian
    • Tsarev, S. P., "Semi-Hamiltonian formalism of diagonal systems of hydrodynamic type and integrability of equations of chromatography and electrophoresis, preprint (LOMI, St. Petersburg, 1989) No. 106, pp. 30-35; "Integration of chromatography equations for Lengmur isoterm of absorption," in Tomographic Methods in Physical-technological Measurement," VNIIFTRI, (1985), pp. 120-125 (in Russian).
    • (1985) Tomographic Methods in Physical-technological Measurement , pp. 120-125
  • 48
    • 0001923961 scopus 로고
    • Benney's equations and quasi-classical approximation in the inverse problem method
    • Zakharov, V. E., "Benney's equations and quasi-classical approximation in the inverse problem method," Funct. Anal. Appl. 14 (2), 89-98 (1980); "On the Benney's equations," Physica D 3, 193-200 (1981).
    • (1980) Funct. Anal. Appl. , vol.14 , Issue.2 , pp. 89-98
    • Zakharov, V.E.1
  • 49
    • 0000314731 scopus 로고
    • On the Benney's equations
    • Zakharov, V. E., "Benney's equations and quasi-classical approximation in the inverse problem method," Funct. Anal. Appl. 14 (2), 89-98 (1980); "On the Benney's equations," Physica D 3, 193-200 (1981).
    • (1981) Physica D , vol.3 , pp. 193-200


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