메뉴 건너뛰기




Volumn 23, Issue 1, 1996, Pages 49-66

On the KdV soliton formation and discrete spectral analysis

Author keywords

[No Author keywords available]

Indexed keywords

DISPERSION (WAVES); EIGENVALUES AND EIGENFUNCTIONS; FINITE DIFFERENCE METHOD; INTEGRATION; INVERSE PROBLEMS; MATHEMATICAL TRANSFORMATIONS; SOLITONS; SPECTRUM ANALYSIS;

EID: 0030073963     PISSN: 01652125     EISSN: None     Source Type: Journal    
DOI: 10.1016/0165-2125(95)00040-2     Document Type: Article
Times cited : (37)

References (46)
  • 1
    • 0001524186 scopus 로고
    • On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves
    • D.J. Korteweg and G. de Vries, "On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves", Phil. Mag. 39, 422-443 (1895).
    • (1895) Phil. Mag. , vol.39 , pp. 422-443
    • Korteweg, D.J.1    De Vries, G.2
  • 2
    • 33846361348 scopus 로고
    • Interaction of solitons in a collisionless plasma and the recurrence of initial states
    • N.J. Zabusky and M.D. Kruskal, "Interaction of solitons in a collisionless plasma and the recurrence of initial states", Phys. Rev. Lett. 15, 240-243 (1965).
    • (1965) Phys. Rev. Lett. , vol.15 , pp. 240-243
    • Zabusky, N.J.1    Kruskal, M.D.2
  • 9
    • 0007218762 scopus 로고
    • On instability of some finite difference schemes for the Korteweg-de Vries equation
    • K. Goda, "On instability of some finite difference schemes for the Korteweg-de Vries equation", J. Phys. Soc. Japan 39, 229-236 (1975).
    • (1975) J. Phys. Soc. Japan , vol.39 , pp. 229-236
    • Goda, K.1
  • 10
    • 0000375325 scopus 로고
    • An explicit finite difference scheme with exact conservation properties
    • J.M. Sanz-Serna, "An explicit finite difference scheme with exact conservation properties", J. Comput. Phys. 47, 199-210 (1982).
    • (1982) J. Comput. Phys. , vol.47 , pp. 199-210
    • Sanz-Serna, J.M.1
  • 11
    • 84968503320 scopus 로고
    • A simplified Galerkin method for hyperbolic equations
    • R.C.Y. Chin, G.W. Hedstrom and K.E. Karlsson, "A simplified Galerkin method for hyperbolic equations", Math. Comput. 33, 647-658 (1979).
    • (1979) Math. Comput. , vol.33 , pp. 647-658
    • Chin, R.C.Y.1    Hedstrom, G.W.2    Karlsson, K.E.3
  • 12
    • 0345501255 scopus 로고
    • A hopscotch method for the Korteweg-de Vries equation
    • I.S. Greig and J.L. Morris, "A hopscotch method for the Korteweg-de Vries equation", J. Comput. Phys. 20, 64-80 (1976).
    • (1976) J. Comput. Phys. , vol.20 , pp. 64-80
    • Greig, I.S.1    Morris, J.L.2
  • 13
    • 0017035968 scopus 로고
    • The application of the spectral method to nonlinear wave propagation
    • H. Shamel and K. Elsässer, "The application of the spectral method to nonlinear wave propagation", J. Comput. Phys. 22, 501-516 (1976).
    • (1976) J. Comput. Phys. , vol.22 , pp. 501-516
    • Shamel, H.1    Elsässer, K.2
  • 14
    • 0018927101 scopus 로고
    • Fourier expansion solution of the Korteweg-de Vries equation
    • K. Abe and O. Inoue, "Fourier expansion solution of the Korteweg-de Vries equation", J. Comput. Phys. 34, 202-210 (1980).
    • (1980) J. Comput. Phys. , vol.34 , pp. 202-210
    • Abe, K.1    Inoue, O.2
  • 15
    • 0000251609 scopus 로고
    • Numerical solutions of the Korteweg-de Vries equation and its generalisations by the split-step Fourier method
    • F. Tappert, "Numerical solutions of the Korteweg-de Vries equation and its generalisations by the split-step Fourier method". Lectures in Appl. Math. 15, 215-216 (1974).
    • (1974) Lectures in Appl. Math. , vol.15 , pp. 215-216
    • Tappert, F.1
  • 16
    • 0015400805 scopus 로고
    • Comparison of pseudospectral and spectral approximation
    • S.A. Orszag, "Comparison of pseudospectral and spectral approximation", Studies in Appl. Math. 51, 253-259 (1972).
    • (1972) Studies in Appl. Math. , vol.51 , pp. 253-259
    • Orszag, S.A.1
  • 17
    • 0000914453 scopus 로고
    • Comparison of accurate methods for the integration of hyperbolic equations
    • H.-O. Kreiss and J. Oliger, "Comparison of accurate methods for the integration of hyperbolic equations", Tellus 24, 199-215 (1972).
    • (1972) Tellus , vol.24 , pp. 199-215
    • Kreiss, H.-O.1    Oliger, J.2
  • 18
    • 0001184056 scopus 로고
    • Stability of the Fourier method
    • H.-O. Kreiss and J. Oliger, "Stability of the Fourier method", SIAM J. Numer. Anal. 16, 421-433 (1979).
    • (1979) SIAM J. Numer. Anal. , vol.16 , pp. 421-433
    • Kreiss, H.-O.1    Oliger, J.2
  • 19
    • 0016555995 scopus 로고
    • On the Fourier method for the integration of hyperbolic equations
    • B. Fornberg, "On the Fourier method for the integration of hyperbolic equations", SIAM J. Numer. Anal. 12, 509-528 (1975).
    • (1975) SIAM J. Numer. Anal. , vol.12 , pp. 509-528
    • Fornberg, B.1
  • 20
    • 0017901962 scopus 로고
    • A numerical and theoretical study of certain nonlinear wave phenomena
    • B. Fornberg and G.B. Whitham, "A numerical and theoretical study of certain nonlinear wave phenomena", Phil. Trans. Roy. Soc. A289, 373-404 (1978).
    • (1978) Phil. Trans. Roy. Soc. , vol.A289 , pp. 373-404
    • Fornberg, B.1    Whitham, G.B.2
  • 21
    • 0001139323 scopus 로고
    • Computational synergetics and mathematical innovation
    • N.J. Zabusky, "Computational synergetics and mathematical innovation", J. Comput. Phys. 43, 195-249 (1981).
    • (1981) J. Comput. Phys. , vol.43 , pp. 195-249
    • Zabusky, N.J.1
  • 22
    • 11744334220 scopus 로고
    • Studies of a non-linear lattice
    • M. Toda, "Studies of a non-linear lattice", Phys. Rep. 18, 1-124 (1975).
    • (1975) Phys. Rep. , vol.18 , pp. 1-124
    • Toda, M.1
  • 23
    • 0000346848 scopus 로고
    • Recurrence of initial state of Korteweg-de Vries equation
    • K. Abe and T. Abe, "Recurrence of initial state of Korteweg-de Vries equation", Phys. Fluids 22, 1644-1646 (1979).
    • (1979) Phys. Fluids , vol.22 , pp. 1644-1646
    • Abe, K.1    Abe, T.2
  • 24
    • 0005356644 scopus 로고
    • Recurrence of initial state of nonlinear ion waves
    • K. Abe and N. Satofuka, "Recurrence of initial state of nonlinear ion waves", Phys. Fluids 24, 1045-1048 (1981).
    • (1981) Phys. Fluids , vol.24 , pp. 1045-1048
    • Abe, K.1    Satofuka, N.2
  • 25
    • 0001276861 scopus 로고
    • On the problem of energy equipartition for large systems of the fermi-pasta-ulam type: Analytical and numerical estimates
    • L. Galgani, A. Giorgilli, A. Martinoli and S. Vanzini, "On the problem of energy equipartition for large systems of the Fermi-Pasta-Ulam type: analytical and numerical estimates", Physica D 59, 334-348 (1992).
    • (1992) Physica D , vol.59 , pp. 334-348
    • Galgani, L.1    Giorgilli, A.2    Martinoli, A.3    Vanzini, S.4
  • 26
    • 0001379378 scopus 로고
    • Nonlinear evolution of disturbances in plasmas and other dispersive media
    • Y.A. Berezin and V.I. Karpman, "Nonlinear evolution of disturbances in plasmas and other dispersive media", Sov. Phys. JETP 24, 1049-1056 (1966).
    • (1966) Sov. Phys. JETP , vol.24 , pp. 1049-1056
    • Berezin, Y.A.1    Karpman, V.I.2
  • 27
    • 84981754671 scopus 로고
    • Integrals of nonlinear equations of evolution and solitary waves
    • P.D. Lax, "Integrals of nonlinear equations of evolution and solitary waves", Comm. Pure Appl. Math. 21, 467-490 (1968).
    • (1968) Comm. Pure Appl. Math. , vol.21 , pp. 467-490
    • Lax, P.D.1
  • 28
    • 0007677339 scopus 로고
    • The exact N-soliton solution of the Korteweg-de Vries equation
    • M. Wadati and M. Toda, "The exact N-soliton solution of the Korteweg-de Vries equation", J. Phys. Soc. Japan 32, 1403-1411 (1972).
    • (1972) J. Phys. Soc. Japan , vol.32 , pp. 1403-1411
    • Wadati, M.1    Toda, M.2
  • 29
    • 0022098032 scopus 로고
    • Internal structure of the two-soliton solution of the KdV equation
    • S. Caenepeel and W. Malfiet, "Internal structure of the two-soliton solution of the KdV equation", Wave Motion 7, 299-305 (1985).
    • (1985) Wave Motion , vol.7 , pp. 299-305
    • Caenepeel, S.1    Malfiet, W.2
  • 30
    • 24444473070 scopus 로고
    • Interaction time of Korteweg-de Vries solitons
    • N. Hatakenaka, "Interaction time of Korteweg-de Vries solitons", Phys. Rev. E 48, 4033-4036 (1993).
    • (1993) Phys. Rev. E , vol.48 , pp. 4033-4036
    • Hatakenaka, N.1
  • 33
    • 0002404627 scopus 로고
    • Identifying coherent structures in nonlinear wave propagation
    • W.I. Newman, D.K. Campbell and J.M. Hyman, "Identifying coherent structures in nonlinear wave propagation", Chaos 1, 77-94 (1991).
    • (1991) Chaos , vol.1 , pp. 77-94
    • Newman, W.I.1    Campbell, D.K.2    Hyman, J.M.3
  • 34
    • 0022075599 scopus 로고
    • Fourier methods with extended stability intervals for the Korteweg-de Vries equation
    • T.F. Chan and T. Kerkhoven, "Fourier methods with extended stability intervals for the Korteweg-de Vries equation", SIAM J. Numer. Anal. 22, 441-454 (1985).
    • (1985) SIAM J. Numer. Anal. , vol.22 , pp. 441-454
    • Chan, T.F.1    Kerkhoven, T.2
  • 35
    • 0039048840 scopus 로고
    • The Fourier pseudospectral method with a restrain operator for the Korteweg-de Vries equation
    • M. He-Ping and G. Ben-Yu, "The Fourier pseudospectral method with a restrain operator for the Korteweg-de Vries equation", J. Comput. Phys. 65, 120-137 (1986).
    • (1986) J. Comput. Phys. , vol.65 , pp. 120-137
    • He-Ping, M.1    Ben-Yu, G.2
  • 36
    • 0039640939 scopus 로고
    • Parametric excitation of computational modes inherent to leap-frog scheme applied to the Korteweg-de Vries equation
    • A. Aoyagi and K. Abe, "Parametric excitation of computational modes inherent to leap-frog scheme applied to the Korteweg-de Vries equation", J. Comput. Phys. 83, 447-462 (1989).
    • (1989) J. Comput. Phys. , vol.83 , pp. 447-462
    • Aoyagi, A.1    Abe, K.2
  • 39
    • 0039048801 scopus 로고
    • On the prediction of the number of solitons excited by an arbitrary potential: An observation from inverse scattering
    • P.J. Hansen and K.E. Lonngren, "On the prediction of the number of solitons excited by an arbitrary potential: An observation from inverse scattering", Physica D 68, 12-17 (1993).
    • (1993) Physica D , vol.68 , pp. 12-17
    • Hansen, P.J.1    Lonngren, K.E.2
  • 40
    • 0005285446 scopus 로고
    • Nonlinear lattice dynamics and energy sharing
    • N.J. Zabusky, "Nonlinear lattice dynamics and energy sharing", J. Phys. Soc. Japan 26, suppl. 196-202 (1969).
    • (1969) J. Phys. Soc. Japan , vol.26 , Issue.SUPPL. , pp. 196-202
    • Zabusky, N.J.1
  • 41
    • 51249186540 scopus 로고
    • Nonlinear Fourier analysis of localized wave fields described by the Korteweg-de Vries equation
    • A.R. Osborne, A, Provenzale and L. Bergamasco, "Nonlinear Fourier analysis of localized wave fields described by the Korteweg-de Vries equation", Il Nuovo Cimento 5, 612-632 (1982).
    • (1982) Il Nuovo Cimento , vol.5 , pp. 612-632
    • Osborne, A.R.1    Provenzale, A.2    Bergamasco, L.3
  • 42
    • 4244103661 scopus 로고
    • Behaviour of solitons in random-function solutions of the periodic Korteweg-de Vries equation
    • A.R. Osborne, "Behaviour of solitons in random-function solutions of the periodic Korteweg-de Vries equation", Phys. Rev. Lett. 71, 3115-3118 (1993).
    • (1993) Phys. Rev. Lett. , vol.71 , pp. 3115-3118
    • Osborne, A.R.1
  • 43
    • 0039640941 scopus 로고
    • The numerical inverse scattering transform for the periodic Korteweg-de Vries equation
    • A.R. Osborne and E. Segre, "The numerical inverse scattering transform for the periodic Korteweg-de Vries equation", Phys. Lett. A 173, 131-142 (1993).
    • (1993) Phys. Lett. A , vol.173 , pp. 131-142
    • Osborne, A.R.1    Segre, E.2
  • 44
    • 0040232804 scopus 로고
    • Korteweg-de Vries soliton detection from a harmonic input
    • A. Salupere, G.A. Maugin and J. Engelbrecht, "Korteweg-de Vries soliton detection from a harmonic input", Phys. Lett. A 192, 5-8 (1994).
    • (1994) Phys. Lett. A , vol.192 , pp. 5-8
    • Salupere, A.1    Maugin, G.A.2    Engelbrecht, J.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.