Multicomponent integrable reductions in the Kadomtsev–Petviashvilli hierarchy

Journal of Mathematical Physics - Tập 34 Số 4 - Trang 1429-1446 - 1993
Jurij Sidorenko1, Walter Strampp2
1University of Lwow, Faculty of Mathematics and Mechanics, 290 000 Lwow, Ukraine
2Fachbereich 17-Mathematik, GH-Universität Kassel, Holländische Str. 36, 3500 Kassel, Germany

Tóm tắt

New types of reductions of the Kadomtsev–Petviashvili (KP) hierarchy are considered on the basis of Sato’s approach. Within this approach the KP hierarchy is represented by infinite sets of equations for potentials u2,u3,..., of pseudodifferential operators and their eigenfunctions Ψ and adjoint eigenfunctions Ψ*. The KP hierarchy was studied under constraints of the following type (∑ni=1 ΨiΨ*i)x = Sκ,x where Sκ,x are symmetries for the KP equation and Ψi(λi), Ψ*i(λi) are eigenfunctions with eigenvalue λi. It is shown that for the first three cases κ=2,3,4 these constraints give rise to hierarchies of 1+1-dimensional commuting flows for the variables u2, Ψ1,...,Ψn, Ψ*1,...,Ψ*n. Bi-Hamiltonian structures for the new hierarchies are presented.

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Tài liệu tham khảo

1983, Publ. RIMS, Kyoto Univ., 19, 943, 10.2977/prims/1195182017

1988, Prog. Theor. Phys. Suppl., 94, 219

1988, J. Phys. A, 21, 743, 10.1088/0305-4470/21/15/001

1988, Inverse Problems, 4, 75

1986, Stud. Appl. Math., 75, 179, 10.1002/sapm1986752179

1988, Commun. Math. Phys., 115, 375, 10.1007/BF01218017

1988, Commun. Math. Phys., 116, 449, 10.1007/BF01229203

1986, Lett. Math. Phys., 12, 171, 10.1007/BF00416506

1990, J. Math. Phys., 31, 1426, 10.1063/1.528732

1990, Lett. Math. Phys., 20, 195, 10.1007/BF00398363

1991, Inverse Problems, 7, L17, 10.1088/0266-5611/7/2/002

1991, Phys. Lett. A, 157, 17, 10.1016/0375-9601(91)90402-T

1991, Inverse Problems, 7, L37, 10.1088/0266-5611/7/6/001

1991, Phys. Lett. A, 157, 22, 10.1016/0375-9601(91)90403-U

1991, J. Phys. A, 24, L1065, 10.1088/0305-4470/24/18/002

1988, Sov. J. Part. Nucl., 19, 252

1974, Commun. Pure Appl. Math., 27, 97, 10.1002/cpa.3160270108

1990, J. Math. Phys., 31, 1374, 10.1063/1.528723

1991, Phys. Lett. A, 160, 149, 10.1016/0375-9601(91)90604-7

1992, Inverse Problems, 245

1992, J. Math. Phys., 33, 2115, 10.1063/1.529632

1992, Phys. Lett. A, 171, 303, 10.1016/0375-9601(92)90648-6

1982, Phys. Lett. A, 88, 323, 10.1016/0375-9601(82)90605-3

1988, Phys. Lett. A, 116, 449

1983, Physica D, 9, 439, 10.1016/0167-2789(83)90283-X

1976, Func. Anal. Appl., 10, 259

1979, Invent. Math., 50, 219

1983, Func. Anal. Appl., 17, 259

1992, Inverse Problems, 8, L13, 10.1088/0266-5611/8/4/003

1992, J. Math. Phys., 33, 3774, 10.1063/1.529875

1976, Progr. Theor. Phys., 56, 1719, 10.1143/PTP.56.1719

1986, Phys. Lett. A, 118, 22, 10.1016/0375-9601(86)90527-X

1983, Lett. Math. Phys., 7, 129, 10.1007/BF00419931

1987, Commun. Math. Phys., 112, 639, 10.1007/BF01225378

1989, Commun. Math. Phys., 120, 451, 10.1007/BF01225507

1982, Phys. Lett. A, 89, 332, 10.1016/0375-9601(82)90186-4

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Journal of Mathematical Physics

Tập 34 Số 4

1429-1446

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