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Volumn 16, Issue 1, 2011, Pages 173-186

A kind of explicit Riemann theta functions periodic waves solutions for discrete soliton equations

Author keywords

Deautonomization of the two dimensional Toda lattice equation; Extended version of the discrete mKdV equation; Periodic wave solution; Theta function solution

Indexed keywords

CRYSTAL LATTICES;

EID: 77955921607     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2010.04.003     Document Type: Article
Times cited : (66)

References (38)
  • 5
    • 34250399331 scopus 로고
    • A periodic problem for the KdV equation
    • Novikov S.P. A periodic problem for the KdV equation. Funct. Anal. Appl. 1974, 8:236-246.
    • (1974) Funct. Anal. Appl. , vol.8 , pp. 236-246
    • Novikov, S.P.1
  • 6
    • 0001531287 scopus 로고
    • Periodic problem for the Kortweg-de Vries equation in the class of finite-band potentials
    • Dubrovin B.A. Periodic problem for the Kortweg-de Vries equation in the class of finite-band potentials. Funct. Anal. Appl. 1975, 9:265-273.
    • (1975) Funct. Anal. Appl. , vol.9 , pp. 265-273
    • Dubrovin, B.A.1
  • 7
    • 0011640108 scopus 로고
    • Hill operators with finitely many gaps
    • Its A., Matveev V.B. Hill operators with finitely many gaps. Funct. Anal. Appl. 1975, 9:65-66.
    • (1975) Funct. Anal. Appl. , vol.9 , pp. 65-66
    • Its, A.1    Matveev, V.B.2
  • 8
    • 84980148156 scopus 로고
    • Periodic solutions of the KdV equation
    • Lax P.D. Periodic solutions of the KdV equation. Commun. Pure. Appl. Math. 1975, 28:141-188.
    • (1975) Commun. Pure. Appl. Math. , vol.28 , pp. 141-188
    • Lax, P.D.1
  • 9
    • 0001253693 scopus 로고
    • The spectrum of Hill's equation
    • Mckean H.P., Moerbeke P. The spectrum of Hill's equation. Invent. Math. 1975, 30:217-274.
    • (1975) Invent. Math. , vol.30 , pp. 217-274
    • Mckean, H.P.1    Moerbeke, P.2
  • 12
    • 0042476346 scopus 로고    scopus 로고
    • The Camassa-Holm hierarchy, N-dimensional integrable systems, and algebro-geometric solution on a symplectic submanifold
    • Qiao Z.J. The Camassa-Holm hierarchy, N-dimensional integrable systems, and algebro-geometric solution on a symplectic submanifold. Commun. Math. Phys. 2003, 239:309-341.
    • (2003) Commun. Math. Phys. , vol.239 , pp. 309-341
    • Qiao, Z.J.1
  • 13
    • 0031518253 scopus 로고    scopus 로고
    • The finite-band solution of the Jaulent-Miodek equation
    • Zhou R.G. The finite-band solution of the Jaulent-Miodek equation. J. Math. Phys. 1997, 38:2535-2546.
    • (1997) J. Math. Phys. , vol.38 , pp. 2535-2546
    • Zhou, R.G.1
  • 14
    • 0033177320 scopus 로고    scopus 로고
    • Relation between the Kadometsev-Petviashvili equation and the confocal involutive system
    • Cao C.W., Wu Y.T., Geng X.G. Relation between the Kadometsev-Petviashvili equation and the confocal involutive system. J. Math. Phys. 1999, 40:3948-3970.
    • (1999) J. Math. Phys. , vol.40 , pp. 3948-3970
    • Cao, C.W.1    Wu, Y.T.2    Geng, X.G.3
  • 15
    • 0033591084 scopus 로고    scopus 로고
    • Quasi-periodic solutions of the modified Kadomtsev-Petviashvili equation
    • Geng X.G., Wu Y.T., Cao C.W. Quasi-periodic solutions of the modified Kadomtsev-Petviashvili equation. J. Phys. A 1999, 32:3733-3742.
    • (1999) J. Phys. A , vol.32 , pp. 3733-3742
    • Geng, X.G.1    Wu, Y.T.2    Cao, C.W.3
  • 18
    • 17744378625 scopus 로고    scopus 로고
    • An algebro-geometric solution for a Hamiltonian system with application to dispersive long wave equation
    • Hon Y.C., Fan E.G. An algebro-geometric solution for a Hamiltonian system with application to dispersive long wave equation. J. Math. Phys. 2005, 46:32701-32721.
    • (2005) J. Math. Phys. , vol.46 , pp. 32701-32721
    • Hon, Y.C.1    Fan, E.G.2
  • 19
    • 0005280965 scopus 로고
    • A direct method of calculating periodic wave solutions to nonlinear evolution equations. I. Exact two-periodic wave solution
    • Nakamura A. A direct method of calculating periodic wave solutions to nonlinear evolution equations. I. Exact two-periodic wave solution. J. Phys. Soc. Jpn 1979, 47:1701-1705.
    • (1979) J. Phys. Soc. Jpn , vol.47 , pp. 1701-1705
    • Nakamura, A.1
  • 20
    • 2742587908 scopus 로고
    • A direct method of calculating periodic wave solutions to nonlinear evolution equations. II. exact one- and two-periodic wave solution of the coupled bilinear equations
    • Nakamura A. A direct method of calculating periodic wave solutions to nonlinear evolution equations. II. exact one- and two-periodic wave solution of the coupled bilinear equations. J. Phys. Soc. Jpn 1980, 48:1365-1370.
    • (1980) J. Phys. Soc. Jpn , vol.48 , pp. 1365-1370
    • Nakamura, A.1
  • 23
    • 43949098266 scopus 로고    scopus 로고
    • A kind of explicit quasi-periodic solution and its limit for the Toda lattice equation
    • Hon Y.C., Fan E.G. A kind of explicit quasi-periodic solution and its limit for the Toda lattice equation. Mod. Phys. Lett. B 2008, 22:547.
    • (2008) Mod. Phys. Lett. B , vol.22 , pp. 547
    • Hon, Y.C.1    Fan, E.G.2
  • 24
    • 52649084769 scopus 로고    scopus 로고
    • Quasi-periodic waves and asymptotic behavior for Bogoyavlenskiis breaking soliton equation in (2+1)-dimensions
    • Fan E.G., Hon Y.C. Quasi-periodic waves and asymptotic behavior for Bogoyavlenskiis breaking soliton equation in (2+1)-dimensions. Phys. Rev. E 2008, 78:36607-36619.
    • (2008) Phys. Rev. E , vol.78 , pp. 36607-36619
    • Fan, E.G.1    Hon, Y.C.2
  • 25
    • 68149099819 scopus 로고    scopus 로고
    • Quasi-periodic waves and an asymptotic property for the asymmetrical Nizhnik-Novikov-Veselov equation
    • Fan E.G. Quasi-periodic waves and an asymptotic property for the asymmetrical Nizhnik-Novikov-Veselov equation. J. Phys. A Math. Theory 2009, 42:95206-95210.
    • (2009) J. Phys. A Math. Theory , vol.42 , pp. 95206-95210
    • Fan, E.G.1
  • 26
    • 68549092614 scopus 로고    scopus 로고
    • Exact one-periodic and two-periodic wave solutions to Hirota bilinear equations in (2+1)-dimensional
    • Ma W.X., Zhou R.G. Exact one-periodic and two-periodic wave solutions to Hirota bilinear equations in (2+1)-dimensional. Mod. Phys. Lett. A 2009, 24(21):1677-1688.
    • (2009) Mod. Phys. Lett. A , vol.24 , Issue.21 , pp. 1677-1688
    • Ma, W.X.1    Zhou, R.G.2
  • 27
    • 0028513850 scopus 로고
    • Superposition of solitons and discrete evolution equation
    • Chow K.W. Superposition of solitons and discrete evolution equation. Phys. Scr. 1994, 50:233-237.
    • (1994) Phys. Scr. , vol.50 , pp. 233-237
    • Chow, K.W.1
  • 28
    • 36449005107 scopus 로고
    • A class of exact periodic solutions of nonlinear envelope equations
    • Chow K.W. A class of exact periodic solutions of nonlinear envelope equations. J. Math. Phys. 1995, 36(8):4125-4137.
    • (1995) J. Math. Phys. , vol.36 , Issue.8 , pp. 4125-4137
    • Chow, K.W.1
  • 29
    • 0035832939 scopus 로고    scopus 로고
    • Periodic solutions for a system of four coupled nonlinear Schroinger equations
    • Chow K.W. Periodic solutions for a system of four coupled nonlinear Schroinger equations. Phys. Lett. A 2001, 285:319-326.
    • (2001) Phys. Lett. A , vol.285 , pp. 319-326
    • Chow, K.W.1
  • 30
    • 0036132365 scopus 로고    scopus 로고
    • A class of doubly periodic waves for nonlinear evolution equations
    • Chow K.W. A class of doubly periodic waves for nonlinear evolution equations. Wave Motion 2002, 35:71-90.
    • (2002) Wave Motion , vol.35 , pp. 71-90
    • Chow, K.W.1
  • 31
    • 76749166658 scopus 로고    scopus 로고
    • Darboux transformation and new periodic wave solutions of generalized derivative nonlinear Schrödinger equation
    • Tian S.F., Zhang T.T., Zhang H.Q. Darboux transformation and new periodic wave solutions of generalized derivative nonlinear Schrödinger equation. Phys. Scr. 2009, 80:065013.
    • (2009) Phys. Scr. , vol.80 , pp. 065013
    • Tian, S.F.1    Zhang, T.T.2    Zhang, H.Q.3
  • 32
    • 76749094607 scopus 로고    scopus 로고
    • Some types of solutions and generalized binary Darboux transformation for the mKP equation with self-consistent sources
    • Tian S.F., Wang Z., Zhang H.Q. Some types of solutions and generalized binary Darboux transformation for the mKP equation with self-consistent sources. J. Math. Anal. Appl. 2010, 366:646-662.
    • (2010) J. Math. Anal. Appl. , vol.366 , pp. 646-662
    • Tian, S.F.1    Wang, Z.2    Zhang, H.Q.3
  • 34
    • 29144490638 scopus 로고    scopus 로고
    • Exact solutions for discrete and ultradiscrete modified KdV equations and their relation to box-ball systems
    • Murata M., Isojima S., Nobe A., Satsuma J. Exact solutions for discrete and ultradiscrete modified KdV equations and their relation to box-ball systems. J. Phys. A: Math. Gen. 2006, 39:L27-L34.
    • (2006) J. Phys. A: Math. Gen. , vol.39
    • Murata, M.1    Isojima, S.2    Nobe, A.3    Satsuma, J.4
  • 36
    • 0041154253 scopus 로고    scopus 로고
    • Two-dimensional soliton cellular automaton of deautonomized Toda-type
    • Nagai A., Tokihiro T., Satsumaa J., Willox R., Kajiwara K. Two-dimensional soliton cellular automaton of deautonomized Toda-type. Phys. Lett. A 1997, 234:301-309.
    • (1997) Phys. Lett. A , vol.234 , pp. 301-309
    • Nagai, A.1    Tokihiro, T.2    Satsumaa, J.3    Willox, R.4    Kajiwara, K.5


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.