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Volumn 26, Issue 4, 2010, Pages 1525-1536

A dual-Petrov-Galerkin method for two integrable fifth-order KdV type equations

Author keywords

Caudrey Dodd Gibbon equation; Dual Petrov Galerkin method; Fifthorder KdV equation; Kaup Kupershmidt equation; Multi soliton

Indexed keywords


EID: 77950240964     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2010.26.1525     Document Type: Article
Times cited : (11)

References (27)
  • 4
    • 0001524303 scopus 로고
    • The prologation structure of a high order Kortewge-de Vries equations
    • R. K. Dodd and J. D. Gibbon, The prologation structure of a high order Kortewge-de Vries equations, Proc. Roy. Soc. Lond. A, 358 (1978), 287-296.
    • (1978) Proc. Roy. Soc. Lond. A , vol.358 , pp. 287-296
    • Dodd, R.K.1    Gibbon, J.D.2
  • 6
    • 34447102560 scopus 로고    scopus 로고
    • On the dual Petrov-Galerkin formulation of the KdV equation on a finite interval
    • O. Goubet and J. Shen, On the dual Petrov-Galerkin formulation of the KdV equation on a finite interval, Adv. Differential Equations, 12 (2007), 221-239.
    • (2007) Adv. Differential Equations , vol.12 , pp. 221-239
    • Goubet, O.1    Shen, J.2
  • 7
    • 0030829213 scopus 로고    scopus 로고
    • Symbolic methods to construct exact solutions of nonlinear partial differential equations
    • W. Hereman and A. Nuseir, Symbolic methods to construct exact solutions of nonlinear partial differential equations, Math. and Comp. in Simu., 43 (1997), 13-27.
    • (1997) Math. and Comp. in Simu. , vol.43 , pp. 13-27
    • Hereman, W.1    Nuseir, A.2
  • 8
    • 36849101831 scopus 로고
    • Exact N-soliton solution of the wave equation of long waves in shallow water and in nonlinear lattices
    • R. Hirota, Exact N-soliton solution of the wave equation of long waves in shallow water and in nonlinear lattices,J. Math. Phys., 14 (1973), 810-814.
    • (1973) J. Math. Phys. , vol.14 , pp. 810-814
    • Hirota, R.1
  • 10
    • 0000219244 scopus 로고
    • Existence of perturbed solitary wave solutions to a model equation for water waves
    • J. K. Hunter and J. Scheurle, Existence of perturbed solitary wave solutions to a model equation for water waves, Phys. D, 32 (1988), 253-268.
    • (1988) Phys. D , vol.32 , pp. 253-268
    • Hunter, J.K.1    Scheurle, J.2
  • 11
    • 0000531288 scopus 로고
    • An extension of nonlinear evolution equations of the KdV (m-KdV) type to higher orders
    • M. Ito, An extension of nonlinear evolution equations of the KdV (m-KdV) type to higher orders, J. Phys. Soc. Japan, 49 (1980), 771-778.
    • (1980) J. Phys. Soc. Japan , vol.49 , pp. 771-778
    • Ito, M.1
  • 12
    • 0002408905 scopus 로고
    • x + 6Rψ= λψ
    • x + 6Rψ= λψ Stdu. Appl. Math., 62 (1980), 189-216.
    • (1980) Stdu. Appl. Math. , vol.62 , pp. 189-216
    • Kaup, D.1
  • 13
    • 77952762814 scopus 로고
    • Oscillatory solitary waves in dispersive media
    • T. Kawahara, Oscillatory solitary waves in dispersive media, J. Phys. Soc. Japan, 33 (1972), 260-264.
    • (1972) J. Phys. Soc. Japan , vol.33 , pp. 260-264
    • Kawahara, T.1
  • 14
    • 44949188352 scopus 로고    scopus 로고
    • The Kawahara-type equation in weighted Sobolev spaces
    • N. Khanal, J. Wu and J.-M. Yuan, The Kawahara-type equation in weighted Sobolev spaces, Nonlinearity, 21 (2008), 1489-1505.
    • (2008) Nonlinearity , vol.21 , pp. 1489-1505
    • Khanal, N.1    Wu, J.2    Yuan, J.-M.3
  • 15
    • 0000106540 scopus 로고    scopus 로고
    • Existence and nonexistence of solitary wave solutions to high-order model evolution equations
    • S. Kichenassamy and P. J. Olver, Existence and nonexistence of solitary wave solutions to high-order model evolution equations, SIAM J. Math. Anal., 23, 1141-1166.
    • SIAM J. Math. Anal. , vol.23 , pp. 1141-1166
    • Kichenassamy, S.1    Olver, P.J.2
  • 16
    • 0001695541 scopus 로고
    • A super KdV equation: An integrable system
    • B. A. Kupershmidt, A super KdV equation: An integrable system, Phys. Lett. A, 102 (1984), 213-215.
    • (1984) Phys. Lett. A , vol.102 , pp. 213-215
    • Kupershmidt, B.A.1
  • 17
    • 84981754671 scopus 로고
    • Integrals of nonlinear equations of evolution and solitary waves
    • P. Lax, Integrals of nonlinear equations of evolution and solitary waves, Comm. Pure Appl. Math., 21 (1968), 467-490.
    • (1968) Comm. Pure Appl. Math. , vol.21 , pp. 467-490
    • Lax, P.1
  • 18
    • 0345846114 scopus 로고    scopus 로고
    • On soliton solutions of the Kaup-Kupershmidt equation. I. Direct bilinearisation and solitary wave
    • A. Parker, On soliton solutions of the Kaup-Kupershmidt equation. I. Direct bilinearisation and solitary wave, Physica D, 137 (2000), 25-33.
    • (2000) Physica D , vol.137 , pp. 25-33
    • Parker, A.1
  • 19
    • 0346684395 scopus 로고    scopus 로고
    • On soliton solutions of the Kaup-Kupershmidt equation. II. 'anomalous' N-soliton solutions
    • A. Parker, On soliton solutions of the Kaup-Kupershmidt equation. II. 'anomalous' N-soliton solutions, Physica D, 137 (2000), 34-48.
    • (2000) Physica D , vol.137 , pp. 34-48
    • Parker, A.1
  • 20
    • 56249129439 scopus 로고
    • A Bäcklund transformation for a higher order Korteweg-de Vries equation
    • J. Satsuma and D. Kaup, A Bäcklund transformation for a higher order Korteweg-de Vries equation, J. Phys. Soc. Japan, 43 (1977), 692-726.
    • (1977) J. Phys. Soc. Japan , vol.43 , pp. 692-726
    • Satsuma, J.1    Kaup, D.2
  • 21
    • 9244255255 scopus 로고    scopus 로고
    • A new dual-Petrov-Galerkin method for third and higher odd-order differential equations: Application to the KdV euqation
    • J. Shen, A new dual-Petrov-Galerkin method for third and higher odd-order differential equations: Application to the KdV euqation, SIAM J. Num. Anal., 41 (2003), 1595-1619.
    • (2003) SIAM J. Num. Anal. , vol.41 , pp. 1595-1619
    • Shen, J.1
  • 22
    • 33750509139 scopus 로고    scopus 로고
    • Logueme and composite Legendre-Laguerre dual-Petrov-Galerkin methods for third-order equations
    • J. Shen and L. L. Wang, Logueme and composite Legendre-Laguerre dual-Petrov-Galerkin methods for third-order equations, DCDS-B, 6 (2006), 1381-1402.
    • (2006) DCDS-B , vol.6 , pp. 1381-1402
    • Shen, J.1    Wang, L.L.2
  • 23
    • 0001395372 scopus 로고
    • A method of finding N-soliton solutions of the KdV and KdV-like equation
    • K. Sawada and T. Kotera, A method of finding N-soliton solutions of the KdV and KdV-like equation, Progr. Theoret. Phys., 51 (1974), 1355-1367.
    • (1974) Progr. Theoret. Phys. , vol.51 , pp. 1355-1367
    • Sawada, K.1    Kotera, T.2
  • 24
    • 0032141594 scopus 로고    scopus 로고
    • On the oscillatory tails with arbitary phase shift for solutions of the perturbed Korteweg-de Vries equation
    • S. M. Sun, On the oscillatory tails with arbitary phase shift for solutions of the perturbed Korteweg-de Vries equation, SIAM J. Appl. Math., 58 (1998), 1163-1177.
    • (1998) SIAM J. Appl. Math. , vol.58 , pp. 1163-1177
    • Sun, S.M.1
  • 25
    • 39449088871 scopus 로고    scopus 로고
    • Multiple-soliton solutions for the fifth-order Caudrey-Dodd-Gibbon (CDG) equation
    • A.-M. Wazwaz, Multiple-soliton solutions for the fifth-order Caudrey-Dodd-Gibbon (CDG) equation, Appl. Math. Comp., 197 (2008), 719-724.
    • (2008) Appl. Math. Comp. , vol.197 , pp. 719-724
    • Wazwaz, A.-M.1
  • 27
    • 37549052189 scopus 로고    scopus 로고
    • A dual-Petrov-Galerkin method for the Kawahara-type equation
    • J.-M. Yuan, J. Shen and J. Wu, A dual-Petrov-Galerkin method for the Kawahara-type equation, J. Sci. Comp., 34 (2008), 48-63.
    • (2008) J. Sci. Comp. , vol.34 , pp. 48-63
    • Yuan, J.-M.1    Shen, J.2    Wu, J.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.