메뉴 건너뛰기




Volumn 52, Issue 3, 2011, Pages

On the constrained B-type Kadomtsev-Petviashvili hierarchy: Hirota bilinear equations and Virasoro symmetry

Author keywords

[No Author keywords available]

Indexed keywords


EID: 79953278086     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3559081     Document Type: Article
Times cited : (45)

References (35)
  • 1
    • 0347308599 scopus 로고    scopus 로고
    • Virasoro symmetry of constrained KP hierarchy
    • 10.1016/S0375-9601(97)00126-6, and,,, .
    • Aratyn H, Nissimov E, Pacheva S. Virasoro symmetry of constrained KP hierarchy. Phys. Lett. A 1997, 228:164. 10.1016/S0375-9601(97)00126-6, and,,, .
    • (1997) Phys. Lett. A , vol.228 , pp. 164
    • Aratyn, H.1    Nissimov, E.2    Pacheva, S.3
  • 2
    • 0001297868 scopus 로고    scopus 로고
    • Constrained KP hierarchies: additional symmetries, Darboux-Bäcklund solutions and relations to multi-matrix models
    • 10.1142/S0217751X97000992, and,,, .
    • Aratyn H, Nissimov E, Pacheva S. Constrained KP hierarchies: additional symmetries, Darboux-Bäcklund solutions and relations to multi-matrix models. Int. J. Mod. Phys. A 1997, 12:1265. 10.1142/S0217751X97000992, and,,, .
    • (1997) Int. J. Mod. Phys. A , vol.12 , pp. 1265
    • Aratyn, H.1    Nissimov, E.2    Pacheva, S.3
  • 3
    • 0032069132 scopus 로고    scopus 로고
    • Method of squared eigenfunction potentials in integrable hierarchies of KP type
    • 10.1007/s002200050338, and,,, .
    • Aratyn H, Nissimov E, Pacheva S. Method of squared eigenfunction potentials in integrable hierarchies of KP type. Commun. Math. Phys. 1998, 193:493. 10.1007/s002200050338, and,,, .
    • (1998) Commun. Math. Phys. , vol.193 , pp. 493
    • Aratyn, H.1    Nissimov, E.2    Pacheva, S.3
  • 4
    • 0031502222 scopus 로고    scopus 로고
    • Solving the constrained KP hierarchy by gauge transformations
    • 10.1063/1.532087, and,,, .
    • Chau LL, Shaw JC, Tu MH. Solving the constrained KP hierarchy by gauge transformations. J. Math. Phys. 1997, 38:4128. 10.1063/1.532087, and,,, .
    • (1997) J. Math. Phys. , vol.38 , pp. 4128
    • Chau, L.L.1    Shaw, J.C.2    Tu, M.H.3
  • 5
    • 77955232743 scopus 로고    scopus 로고
    • The "Ghost" symmetry of the BKP hierarchy
    • 10.1063/1.3397943, and,,, .
    • Cheng JP, He JS, Hu S. The "Ghost" symmetry of the BKP hierarchy. J. Math. Phys. 2010, 51:053514. 10.1063/1.3397943, and,,, .
    • (2010) J. Math. Phys. , vol.51 , pp. 053514
    • Cheng, J.P.1    He, J.S.2    Hu, S.3
  • 6
    • 36449006460 scopus 로고
    • Constraints of the Kadomtsev-Petviashvili hierarchy
    • 10.1063/1.529875, .
    • Cheng Y. Constraints of the Kadomtsev-Petviashvili hierarchy. J. Math. Phys. 1992, 33:3774. 10.1063/1.529875, .
    • (1992) J. Math. Phys. , vol.33 , pp. 3774
    • Cheng, Y.1
  • 7
    • 21844504348 scopus 로고
    • Modifying the KP,nth constrained KP hierarchies and their hamiltonian structures
    • 10.1007/BF02104682, .
    • Cheng Y. Modifying the KP,nth constrained KP hierarchies and their hamiltonian structures. Commun. Math. Phys. 1995, 171:661. 10.1007/BF02104682, .
    • (1995) Commun. Math. Phys. , vol.171 , pp. 661
    • Cheng, Y.1
  • 8
    • 0002129325 scopus 로고
    • Bilinear equations for the constrained KP hierarchy
    • 10.1088/0266-5611/10/2/001, and,,, .
    • Cheng Y, Zhang YJ. Bilinear equations for the constrained KP hierarchy. Inverse Probl. Eng. 1994, 10:L11. 10.1088/0266-5611/10/2/001, and,,, .
    • (1994) Inverse Probl. Eng. , vol.10
    • Cheng, Y.1    Zhang, Y.J.2
  • 10
    • 0040503295 scopus 로고
    • On the constrained KP hierarchy
    • 10.1007/BF00750069, .
    • Dickey LA. On the constrained KP hierarchy. Lett. Math. Phys. 1995, 34:379. 10.1007/BF00750069, .
    • (1995) Lett. Math. Phys. , vol.34 , pp. 379
    • Dickey, L.A.1
  • 12
    • 0001476436 scopus 로고    scopus 로고
    • Dispersionful analogues of Benny's equations and N-wave systems
    • 10.1088/0266-5611/12/3/005, and,,,
    • Enriquez B, Orlov A, Rubtsov VN. Dispersionful analogues of Benny's equations and N-wave systems. Inverse Probl. Eng. 1996, 12:241. 10.1088/0266-5611/12/3/005, and,,,.
    • (1996) Inverse Probl. Eng. , vol.12 , pp. 241
    • Enriquez, B.1    Orlov, A.2    Rubtsov, V.N.3
  • 13
    • 0002806571 scopus 로고
    • Virasoro action on Riemann surfaces, Grassmannians, ∂ ̄ and Segal-Wilson tau-function
    • Belavin, A.A., Klimyk, A.U., Zamolodchikov, A.B., and,, in edited by,, and (Springer, Berlin)
    • Grinevich PG, Orlov A. Virasoro action on Riemann surfaces, Grassmannians, ∂̄ and Segal-Wilson tau-function. Problems of Modern Quantum Field Theory 1989, 86. Belavin, A.A., Klimyk, A.U., Zamolodchikov, A.B., and,, in edited by,, and (Springer, Berlin), pp.
    • (1989) Problems of Modern Quantum Field Theory , pp. 86
    • Grinevich, P.G.1    Orlov, A.2
  • 14
    • 34548268608 scopus 로고    scopus 로고
    • Additional symmetries and string equation of the CKP hierarchy
    • 10.1007/s11005-007-0171-1, and,,, .
    • He JS, Tian KL, Foerster A, Ma WX. Additional symmetries and string equation of the CKP hierarchy. Lett. Math. Phys. 2007, 81:119. 10.1007/s11005-007-0171-1, and,,, .
    • (2007) Lett. Math. Phys. , vol.81 , pp. 119
    • He, J.S.1    Tian, K.L.2    Foerster, A.3    Ma, W.X.4
  • 15
    • 36749083007 scopus 로고    scopus 로고
    • Gauge transformations for the constrained CKP and BKP hierarchies
    • 10.1063/1.2817827, and,,, .
    • He JS, Wu ZW, Cheng Y. Gauge transformations for the constrained CKP and BKP hierarchies. J. Math. Phys. 2007, 48:113519. 10.1063/1.2817827, and,,, .
    • (2007) J. Math. Phys. , vol.48 , pp. 113519
    • He, J.S.1    Wu, Z.W.2    Cheng, Y.3
  • 16
    • 0032073617 scopus 로고    scopus 로고
    • An analytic description of the vector constrained KP hierarchy
    • 10.1007/s002200050341, and,,, .
    • Helminck GF, van de Leur J. An analytic description of the vector constrained KP hierarchy. Commun. Math. Phys. 1998, 193:627. 10.1007/s002200050341, and,,, .
    • (1998) Commun. Math. Phys. , vol.193 , pp. 627
    • Helminck, G.F.1    van de Leur, J.2
  • 17
    • 30444449850 scopus 로고    scopus 로고
    • The Direct Method in Soliton theory
    • in (Cambridge University Press, Cambridge), Vol. 155.
    • Hirota R. The Direct Method in Soliton theory. Cambridge Tracts in Mathematics 2004, in (Cambridge University Press, Cambridge), Vol. 155.
    • (2004) Cambridge Tracts in Mathematics
    • Hirota, R.1
  • 18
    • 0003193362 scopus 로고    scopus 로고
    • The Geometry of Spinors and the Multicomponent BKP and DKP Hierarchies
    • and,,, .
    • Kac V, van de Leur J. The Geometry of Spinors and the Multicomponent BKP and DKP Hierarchies. CRM Proceedings and Lecture Notes 1998, 14:159. and,,, .
    • (1998) CRM Proceedings and Lecture Notes , vol.14 , pp. 159
    • Kac, V.1    van de Leur, J.2
  • 19
    • 0041030813 scopus 로고    scopus 로고
    • Dimensional reductions of BKP and CKP hierarchies
    • 10.1088/0305-4470/34/16/313, .
    • Loris I. Dimensional reductions of BKP and CKP hierarchies. J. Phys. A 2001, 34:3447. 10.1088/0305-4470/34/16/313, .
    • (2001) J. Phys. A , vol.34 , pp. 3447
    • Loris, I.1
  • 20
    • 0009291187 scopus 로고    scopus 로고
    • Bilinear form and solutions of the k-constrained Kadomtsev-Petviashvili hierarchy
    • 10.1088/0266-5611/13/2/014, and,,, .
    • Loris I, Willox R. Bilinear form and solutions of the k-constrained Kadomtsev-Petviashvili hierarchy. Inverse Probl. Eng. 1997, 13:411. 10.1088/0266-5611/13/2/014, and,,, .
    • (1997) Inverse Probl. Eng. , vol.13 , pp. 411
    • Loris, I.1    Willox, R.2
  • 21
    • 0033241377 scopus 로고    scopus 로고
    • Symmetry reduction of the BKP hierarchy
    • 10.1063/1.532812, and,,, .
    • Loris I, Willox R. Symmetry reduction of the BKP hierarchy. J. Math. Phys. 1999, 40:1420. 10.1063/1.532812, and,,, .
    • (1999) J. Math. Phys. , vol.40 , pp. 1420
    • Loris, I.1    Willox, R.2
  • 22
    • 0001037040 scopus 로고
    • Darboux theorems and Wronskian formulas for integrable system I: constrained KP flows
    • 10.1016/0378-4371(93)90174-3, ,
    • Oevel W. Darboux theorems and Wronskian formulas for integrable system I: constrained KP flows. Physica A 1993, 12:533. 10.1016/0378-4371(93)90174-3, ,.
    • (1993) Physica A , vol.12 , pp. 533
    • Oevel, W.1
  • 23
    • 21344479834 scopus 로고
    • Constrained KP hierarchy and bi-hamiltonian structures
    • 10.1007/BF02098018, and,,, .
    • Oevel W, Strampp W. Constrained KP hierarchy and bi-hamiltonian structures. Comm. Math. Phys. 1993, 157:51. 10.1007/BF02098018, and,,, .
    • (1993) Comm. Math. Phys. , vol.157 , pp. 51
    • Oevel, W.1    Strampp, W.2
  • 24
    • 0002918206 scopus 로고
    • Volterra operators for zero curvature representation. Universality of KP
    • Fokas, A., Kaup, D., Newell, A., Zakharov, V.E., in, edited by,,, and (Springer Series in Nonlinear Dynamics)
    • Orlov A. Volterra operators for zero curvature representation. Universality of KP. Plasma Theory and Nonlinear and Turbulent Processes in Physics 1993, 126-131. Fokas, A., Kaup, D., Newell, A., Zakharov, V.E., in, edited by,,, and (Springer Series in Nonlinear Dynamics), pp.
    • (1993) Plasma Theory and Nonlinear and Turbulent Processes in Physics , pp. 126-131
    • Orlov, A.1
  • 25
    • 0039650631 scopus 로고
    • Dressing method, Darboux transformation and generalized restricted flows for the KdV hierarchy
    • 10.1016/0167-2789(93)90181-Y, and,,, .
    • Orlov A, Rauch-Wojciechowski S. Dressing method, Darboux transformation and generalized restricted flows for the KdV hierarchy. Physica D 1993, 69:77. 10.1016/0167-2789(93)90181-Y, and,,, .
    • (1993) Physica D , vol.69 , pp. 77
    • Orlov, A.1    Rauch-Wojciechowski, S.2
  • 26
    • 0009145135 scopus 로고
    • Additional symmetries for integrable systems and conformal algebra representation
    • 10.1007/BF00416506, and,,, .
    • Orlov A, Schulman EI. Additional symmetries for integrable systems and conformal algebra representation. Lett. Math. Phys. 1993, 12:171. 10.1007/BF00416506, and,,, .
    • (1993) Lett. Math. Phys. , vol.12 , pp. 171
    • Orlov, A.1    Schulman, E.I.2
  • 27
    • 0031478866 scopus 로고    scopus 로고
    • Algebra of pseudodifferential operators and symmetries of equations in the Kadomtsev-Petviashvili hierarchy
    • 10.1063/1.532112, and,,, .
    • Orlov A, Winternitz P. Algebra of pseudodifferential operators and symmetries of equations in the Kadomtsev-Petviashvili hierarchy. J. Math. Phys. 1997, 38:4644. 10.1063/1.532112, and,,, .
    • (1997) J. Math. Phys. , vol.38 , pp. 4644
    • Orlov, A.1    Winternitz, P.2
  • 28
    • 69849110854 scopus 로고    scopus 로고
    • On the string equation of the BKP hierarchy
    • 10.1142/S0217751X09043390, and,,, .
    • Shen HF, Tu MH. On the string equation of the BKP hierarchy. Int. J. Mod. Phys. A 2009, 24:4193. 10.1142/S0217751X09043390, and,,, .
    • (2009) Int. J. Mod. Phys. A , vol.24 , pp. 4193
    • Shen, H.F.1    Tu, M.H.2
  • 30
    • 0005199059 scopus 로고
    • Quasi-classical limit of BKP hierarchy and W-infinity symmetries
    • 10.1007/BF00745149, .
    • Takasaki K. Quasi-classical limit of BKP hierarchy and W-infinity symmetries. Lett. Math. Phys. 1993, 28:177. 10.1007/BF00745149, .
    • (1993) Lett. Math. Phys. , vol.28 , pp. 177
    • Takasaki, K.1
  • 31
    • 34548218324 scopus 로고    scopus 로고
    • On the BKP hierarchy: additional symmetries, Fay identity and Adler-Shiota-van Moerbeke formula
    • 10.1007/s11005-007-0172-0, .
    • Tu MH. On the BKP hierarchy: additional symmetries, Fay identity and Adler-Shiota-van Moerbeke formula. Lett. Math. Phys. 2007, 81:91. 10.1007/s11005-007-0172-0, .
    • (2007) Lett. Math. Phys. , vol.81 , pp. 91
    • Tu, M.H.1
  • 32
    • 21844520752 scopus 로고
    • The Adler-Shiota-van Moerbeke formula for the BKP hierarchy
    • 10.1063/1.531352, van de,,, .
    • Leur J. The Adler-Shiota-van Moerbeke formula for the BKP hierarchy. J. Math. Phys. 1995, 36:4940. 10.1063/1.531352, van de,,, .
    • (1995) J. Math. Phys. , vol.36 , pp. 4940
    • Leur, J.1
  • 33
    • 0031206162 scopus 로고    scopus 로고
    • The vector k-constrained KP hierarchy and Sato's grassmannian
    • 10.1016/S0393-0440(97)81154-0, .
    • van de Leur J. The vector k-constrained KP hierarchy and Sato's grassmannian. J. Geom. Phys. 1997, 23:83. 10.1016/S0393-0440(97)81154-0, .
    • (1997) J. Geom. Phys. , vol.23 , pp. 83
    • van de Leur, J.1
  • 34
    • 0002874030 scopus 로고    scopus 로고
    • On Segal-Wilson's construction for the τ-functions of the constrained KP hierarchies
    • 10.1007/BF00403246, .
    • Zhang YJ. On Segal-Wilson's construction for the τ-functions of the constrained KP hierarchies. Lett. Math. Phys. 1996, 36:1. 10.1007/BF00403246, .
    • (1996) Lett. Math. Phys. , vol.36 , pp. 1
    • Zhang, Y.J.1
  • 35
    • 36449003797 scopus 로고
    • Solutions for the vector k-constrained KP hierarchy
    • 10.1063/1.530716, and,,, .
    • Zhang YJ, Cheng Y. Solutions for the vector k-constrained KP hierarchy. J. Math. Phys. 1994, 35:5869. 10.1063/1.530716, and,,, .
    • (1994) J. Math. Phys. , vol.35 , pp. 5869
    • Zhang, Y.J.1    Cheng, Y.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.