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Volumn 202, Issue 1 SPECIAL ISSUE, 2007, Pages 133-143

2D Toda lattice equation with self-consistent sources: Casoratian type solutions, bilinear Bäcklund transformation and Lax pair

Author keywords

B cklund transformation and Lax pair; Soliton solutions; Toda lattice with sources

Indexed keywords

INTEGRAL EQUATIONS; MATHEMATICAL TRANSFORMATIONS;

EID: 33749021235     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2005.08.052     Document Type: Article
Times cited : (24)

References (34)
  • 1
    • 0008028742 scopus 로고
    • Soliton hierarchies with sources and Lax representation for restricted flows
    • Antonowicz M., and Rauch-Wojciechowski S. Soliton hierarchies with sources and Lax representation for restricted flows. Inverse Problems 9 (1993) 201-215
    • (1993) Inverse Problems , vol.9 , pp. 201-215
    • Antonowicz, M.1    Rauch-Wojciechowski, S.2
  • 2
    • 0242592215 scopus 로고    scopus 로고
    • The multisoliton solutions of the KP equation with self-consistent sources
    • Deng S.F., Chen D.Y., and Zhang D.J. The multisoliton solutions of the KP equation with self-consistent sources. J. Phys. Soc. Japan 72 (2003) 2184-2192
    • (2003) J. Phys. Soc. Japan , vol.72 , pp. 2184-2192
    • Deng, S.F.1    Chen, D.Y.2    Zhang, D.J.3
  • 3
    • 33745887479 scopus 로고    scopus 로고
    • Gegenhasi, X.B. Hu, On a integrable differential-difference equation with a source, J. Nonlinear Math. Phys. 13(2) (2006), in press.
  • 4
    • 33847075818 scopus 로고    scopus 로고
    • Gegenhasi, X.B. Hu, Integrability of a Differential-Difference KP Equation with Self-consistent Sources, 2005 preprint.
  • 5
    • 2042418503 scopus 로고
    • Soliton solutions of the Mel'nikov equations
    • Hase Y., Hirota R., Ohta Y., and Satsuma J. Soliton solutions of the Mel'nikov equations. J. Phys. Soc. Japan 58 8 (1989) 2713-2720
    • (1989) J. Phys. Soc. Japan , vol.58 , Issue.8 , pp. 2713-2720
    • Hase, Y.1    Hirota, R.2    Ohta, Y.3    Satsuma, J.4
  • 6
    • 33847070392 scopus 로고    scopus 로고
    • R. Hirota, Direct method in soliton theory (in English), (Edited and Translated by A. Nagai, J. Nimmo, C. Gilson, Cambridge University Press, Cambridge, 2004.6).
  • 7
    • 0042791644 scopus 로고
    • Nonlinear superposition formula of the KdV equation with a source
    • Hu X.B. Nonlinear superposition formula of the KdV equation with a source. J. Phys. A 24 (1991) 5489-5497
    • (1991) J. Phys. A , vol.24 , pp. 5489-5497
    • Hu, X.B.1
  • 8
    • 0043127036 scopus 로고    scopus 로고
    • The higher-order KdV equation with a source and nonlinear superposition formula
    • Hu X.B. The higher-order KdV equation with a source and nonlinear superposition formula. Chaos Solitons Fractals 7 (1996) 211-215
    • (1996) Chaos Solitons Fractals , vol.7 , pp. 211-215
    • Hu, X.B.1
  • 9
    • 0000466556 scopus 로고
    • Solution of an initial-boundary value problem for coupled nonlinear waves
    • Leon J., and Latifi A. Solution of an initial-boundary value problem for coupled nonlinear waves. J. Phys. A 23 (1990) 1385-1403
    • (1990) J. Phys. A , vol.23 , pp. 1385-1403
    • Leon, J.1    Latifi, A.2
  • 10
    • 0035280491 scopus 로고    scopus 로고
    • Solving the KdV hierarchy with self-consistent sources by inverse scattering method
    • Lin R.L., Zeng Y.B., and Ma W.X. Solving the KdV hierarchy with self-consistent sources by inverse scattering method. Physica A 291 (2001) 287-298
    • (2001) Physica A , vol.291 , pp. 287-298
    • Lin, R.L.1    Zeng, Y.B.2    Ma, W.X.3
  • 11
    • 0842290212 scopus 로고    scopus 로고
    • Soliton, positon and negaton solutions to a Schrödinger self-consistent source equation
    • Ma W.X. Soliton, positon and negaton solutions to a Schrödinger self-consistent source equation. J. Phys. Soc. Japan 72 (2003) 3017-3019
    • (2003) J. Phys. Soc. Japan , vol.72 , pp. 3017-3019
    • Ma, W.X.1
  • 12
    • 0002796975 scopus 로고
    • An explicit symmetry constraint for the Lax pairs and the adjoint Lax pairs of AKNS systems
    • Ma W.X., and Strampp W. An explicit symmetry constraint for the Lax pairs and the adjoint Lax pairs of AKNS systems. Phys. Lett. A 185 (1994) 277-286
    • (1994) Phys. Lett. A , vol.185 , pp. 277-286
    • Ma, W.X.1    Strampp, W.2
  • 13
    • 0035458179 scopus 로고    scopus 로고
    • Binary symmetry constraints of N wave interaction equations in 1 + 1 and 2 + 1 dimensions
    • Ma W.X., and Zhou Z.X. Binary symmetry constraints of N wave interaction equations in 1 + 1 and 2 + 1 dimensions. J. Math. Phys. 42 (2001) 4345-4382
    • (2001) J. Math. Phys. , vol.42 , pp. 4345-4382
    • Ma, W.X.1    Zhou, Z.X.2
  • 14
    • 14944386086 scopus 로고
    • KP equation with a source and its soliton solutions
    • Matsuno Y. KP equation with a source and its soliton solutions. J. Phys. A 23 (1990) L1235-L1239
    • (1990) J. Phys. A , vol.23
    • Matsuno, Y.1
  • 15
    • 4243905860 scopus 로고
    • Bilinear Bäcklund transformation for the KdV equation with a source
    • Matsuno Y. Bilinear Bäcklund transformation for the KdV equation with a source. J. Phys. A 24 (1991) L273-L277
    • (1991) J. Phys. A , vol.24
    • Matsuno, Y.1
  • 16
    • 0038086928 scopus 로고
    • A direct method for deriving a multi-soliton solution for the problem of interaction of waves on the x, y plane
    • Mel'nikov V.K. A direct method for deriving a multi-soliton solution for the problem of interaction of waves on the x, y plane. Commun. Math. Phys. 112 (1987) 639-652
    • (1987) Commun. Math. Phys. , vol.112 , pp. 639-652
    • Mel'nikov, V.K.1
  • 17
    • 0004625487 scopus 로고
    • Exact solutions of the Korteweg-de Vries equation with a self-consistent source
    • Mel'nikov V.K. Exact solutions of the Korteweg-de Vries equation with a self-consistent source. Phys. Lett. A 128 (1988) 488-492
    • (1988) Phys. Lett. A , vol.128 , pp. 488-492
    • Mel'nikov, V.K.1
  • 18
    • 0001711435 scopus 로고
    • Interaction of solitary waves in the system described by the Kadomtsev-Petviashvili equation with a self-consistent source
    • Mel'nikov V.K. Interaction of solitary waves in the system described by the Kadomtsev-Petviashvili equation with a self-consistent source. Commun. Math. Phys. 126 (1989) 201-215
    • (1989) Commun. Math. Phys. , vol.126 , pp. 201-215
    • Mel'nikov, V.K.1
  • 19
    • 0000458161 scopus 로고
    • Capture and confinement of solitons in nonlinear integrable systems
    • Mel'nikov V.K. Capture and confinement of solitons in nonlinear integrable systems. Commun. Math. Phys. 120 (1989) 451-468
    • (1989) Commun. Math. Phys. , vol.120 , pp. 451-468
    • Mel'nikov, V.K.1
  • 20
    • 0001195220 scopus 로고
    • Integration of the Korteweg-de Vries equation with a source
    • Mel'nikov V.K. Integration of the Korteweg-de Vries equation with a source. Inverse Problems 6 (1990) 233-246
    • (1990) Inverse Problems , vol.6 , pp. 233-246
    • Mel'nikov, V.K.1
  • 21
    • 0035540418 scopus 로고    scopus 로고
    • Integration of the Korteweg-de Vries equation with a self-consistent source in the presence of "steplike" initial data
    • Urasboev G.U., and Khasanov A.B. Integration of the Korteweg-de Vries equation with a self-consistent source in the presence of "steplike" initial data. Theoret. Math. Phys. 129 (2001) 1341-1356
    • (2001) Theoret. Math. Phys. , vol.129 , pp. 1341-1356
    • Urasboev, G.U.1    Khasanov, A.B.2
  • 22
    • 33847073087 scopus 로고    scopus 로고
    • H.Y. Wang, Some results on the semi-discrete Toda equation with self-consistent sources, 2005, preprint.
  • 23
    • 3242661001 scopus 로고    scopus 로고
    • Generalized Darboux transformations for the KP equation with self-consistent sources
    • Xiao T., and Zeng Y.B. Generalized Darboux transformations for the KP equation with self-consistent sources. J. Phys. A 37 (2004) 7143
    • (2004) J. Phys. A , vol.37 , pp. 7143
    • Xiao, T.1    Zeng, Y.B.2
  • 24
    • 18844411640 scopus 로고    scopus 로고
    • A new constrained mKP hierarchy and the generalized Darboux transformation for the mKP equation with self-consistent sources
    • Xiao T., and Zeng Y.B. A new constrained mKP hierarchy and the generalized Darboux transformation for the mKP equation with self-consistent sources. Physica A 353 (2005) 38-60
    • (2005) Physica A , vol.353 , pp. 38-60
    • Xiao, T.1    Zeng, Y.B.2
  • 25
    • 0037205279 scopus 로고    scopus 로고
    • Integration of the modified Korteweg-de Vries hierarchy with an integral type of source
    • Ye S., and Zeng Y.B. Integration of the modified Korteweg-de Vries hierarchy with an integral type of source. J. Phys. A 35 (2002) L283-L291
    • (2002) J. Phys. A , vol.35
    • Ye, S.1    Zeng, Y.B.2
  • 26
    • 43949150163 scopus 로고
    • New factorization of the Kaup-Newell hierarchy
    • Zeng Y.B. New factorization of the Kaup-Newell hierarchy. Physica D 73 (1994) 171-188
    • (1994) Physica D , vol.73 , pp. 171-188
    • Zeng, Y.B.1
  • 27
    • 0001102697 scopus 로고    scopus 로고
    • The Lax representation and Darboux transformation for constrained flows of the AKNS hierarchy
    • Zeng Y.B., and Li Y.S. The Lax representation and Darboux transformation for constrained flows of the AKNS hierarchy. Acta Math. Sinica, New Ser. 12 (1996) 217-224
    • (1996) Acta Math. Sinica, New Ser. , vol.12 , pp. 217-224
    • Zeng, Y.B.1    Li, Y.S.2
  • 28
    • 0034238372 scopus 로고    scopus 로고
    • Integration of the soliton hierarchy with self-consistent sources
    • Zeng Y.B., Ma W.X., and Lin R.L. Integration of the soliton hierarchy with self-consistent sources. J. Math. Phys. 41 (2000) 5453-5489
    • (2000) J. Math. Phys. , vol.41 , pp. 5453-5489
    • Zeng, Y.B.1    Ma, W.X.2    Lin, R.L.3
  • 29
    • 0034238372 scopus 로고    scopus 로고
    • Integration of the soliton hierarchy with self-consistent sources
    • Zeng Y.B., Ma W.X., and Lin R.L. Integration of the soliton hierarchy with self-consistent sources. J. Math. Phys. 41 (2000) 5453-5489
    • (2000) J. Math. Phys. , vol.41 , pp. 5453-5489
    • Zeng, Y.B.1    Ma, W.X.2    Lin, R.L.3
  • 30
    • 0035633743 scopus 로고    scopus 로고
    • Two binary Darboux transformations for the KdV hierarchy with self-consistent sources
    • Zeng Y.B., Ma W.X., and Shao Y.J. Two binary Darboux transformations for the KdV hierarchy with self-consistent sources. J. Math. Phys. 42 (2001) 2113-2128
    • (2001) J. Math. Phys. , vol.42 , pp. 2113-2128
    • Zeng, Y.B.1    Ma, W.X.2    Shao, Y.J.3
  • 31
    • 0036883317 scopus 로고    scopus 로고
    • Integrable-type Darboux transformation for the mKdV hierarchy with self-consistent sources
    • Zeng Y.B., Shao Y.J., and Ma W.X. Integrable-type Darboux transformation for the mKdV hierarchy with self-consistent sources. Commun. Theoret. Phys. Beijing 38 (2002) 641-648
    • (2002) Commun. Theoret. Phys. Beijing , vol.38 , pp. 641-648
    • Zeng, Y.B.1    Shao, Y.J.2    Ma, W.X.3
  • 32
    • 0036967839 scopus 로고    scopus 로고
    • The N-soliton solutions for the modified KdV equation with self-consistent sources
    • Zhang D.J. The N-soliton solutions for the modified KdV equation with self-consistent sources. J. Phys. Soc. Japan 71 (2002) 2649-2656
    • (2002) J. Phys. Soc. Japan , vol.71 , pp. 2649-2656
    • Zhang, D.J.1
  • 33
    • 0037884829 scopus 로고    scopus 로고
    • The N-soliton solutions of some soliton equations with self-consistent sources
    • Zhang D.J. The N-soliton solutions of some soliton equations with self-consistent sources. Chaos, Solitons Fractals 18 (2003) 31-43
    • (2003) Chaos, Solitons Fractals , vol.18 , pp. 31-43
    • Zhang, D.J.1
  • 34
    • 0037446056 scopus 로고    scopus 로고
    • The N-soliton solutions of the sine-Gordon equation with self-consistent sources
    • Zhang D.J., and Chen D.Y. The N-soliton solutions of the sine-Gordon equation with self-consistent sources. Physica A 321 (2003) 467-481
    • (2003) Physica A , vol.321 , pp. 467-481
    • Zhang, D.J.1    Chen, D.Y.2


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