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Volumn 15, Issue 1, 1999, Pages 215-240

Perturbation theory for the Benjamin-Ono equation

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EID: 0002613498     PISSN: 02665611     EISSN: None     Source Type: Journal    
DOI: 10.1088/0266-5611/15/1/022     Document Type: Article
Times cited : (20)

References (35)
  • 1
    • 84902775564 scopus 로고
    • Internal waves of permanent form in fluids of great depth
    • Benjamin T B 1967 Internal waves of permanent form in fluids of great depth J. Fluid Mech. 29 559
    • (1967) J. Fluid Mech. , vol.29 , pp. 559
    • Benjamin, T.B.1
  • 2
    • 77955587949 scopus 로고
    • Solitary internal waves in deep water
    • Davies R E and Acrivos A 1967 Solitary internal waves in deep water J. Fluid Mech. 29 593
    • (1967) J. Fluid Mech. , vol.29 , pp. 593
    • Davies, R.E.1    Acrivos, A.2
  • 3
    • 0016459710 scopus 로고
    • Algebraic solitary waves in stratified fluids
    • Ono H 1975 Algebraic solitary waves in stratified fluids J. Phys. Soc. Japan 39 1082
    • (1975) J. Phys. Soc. Japan , vol.39 , pp. 1082
    • Ono, H.1
  • 4
    • 0000246483 scopus 로고
    • Linear stability of internal wave solitons in a deep stratified fluid
    • Chen H H and Kaup D J 1980 Linear stability of internal wave solitons in a deep stratified fluid Phys. Fluids 23 235
    • (1980) Phys. Fluids , vol.23 , pp. 235
    • Chen, H.H.1    Kaup, D.J.2
  • 5
    • 0000454566 scopus 로고
    • Multisoliton perturbation theory for the Benjamin-Ono equation and its applications to real physical systems
    • Matsuno Y 1995 Multisoliton perturbation theory for the Benjamin-Ono equation and its applications to real physical systems Phys. Rev. E 51 1471
    • (1995) Phys. Rev. E , vol.51 , pp. 1471
    • Matsuno, Y.1
  • 6
    • 0000164801 scopus 로고    scopus 로고
    • Linear stability of multiple internal solitary waves in fluids of great depth
    • Matsuno Y and Kaup D J 1997 Linear stability of multiple internal solitary waves in fluids of great depth Phys. Lett. A 228 176
    • (1997) Phys. Lett. A , vol.228 , pp. 176
    • Matsuno, Y.1    Kaup, D.J.2
  • 7
    • 0031534144 scopus 로고    scopus 로고
    • Initial value problem of the linearized Benjamin-Ono equation and its applications
    • Matsuno Y and Kaup D J 1997 Initial value problem of the linearized Benjamin-Ono equation and its applications J. Math. Phys. 38 5198
    • (1997) J. Math. Phys. , vol.38 , pp. 5198
    • Matsuno, Y.1    Kaup, D.J.2
  • 8
    • 0020706321 scopus 로고
    • The inverse scattering transform for the Benjamin-Ono equation - A pivot to multidimensional problems
    • Fokas A S and Ablowitz M J 1983 The inverse scattering transform for the Benjamin-Ono equation - a pivot to multidimensional problems Stud. Appl. Math. 68 1
    • (1983) Stud. Appl. Math. , vol.68 , pp. 1
    • Fokas, A.S.1    Ablowitz, M.J.2
  • 9
    • 21844490365 scopus 로고
    • On the initial value problem for the modified Benjamin-Ono equation
    • Scoufis G and Cosgrove C M 1995 On the initial value problem for the modified Benjamin-Ono equation J. Math. Phys. 36 5753
    • (1995) J. Math. Phys. , vol.36 , pp. 5753
    • Scoufis, G.1    Cosgrove, C.M.2
  • 10
    • 0039528885 scopus 로고    scopus 로고
    • On the IST for the Benjamin-Ono equation
    • Kaup D J and Matsuno Y 1998 On the IST for the Benjamin-Ono equation Stud. Appl. Math. 101 73
    • (1998) Stud. Appl. Math. , vol.101 , pp. 73
    • Kaup, D.J.1    Matsuno, Y.2
  • 11
    • 0002607322 scopus 로고    scopus 로고
    • Complete integrability of the Benjamin-Ono equation by means of action-angle variables
    • Kaup D J, Lakoba T I and Matsuno Y 1998 Complete integrability of the Benjamin-Ono equation by means of action-angle variables Phys. Lett. A 238 123
    • (1998) Phys. Lett. A , vol.238 , pp. 123
    • Kaup, D.J.1    Lakoba, T.I.2    Matsuno, Y.3
  • 12
    • 0005760999 scopus 로고
    • The scattering transform for the Benjamin-Ono equation
    • Coifman R R and Wickerhauser M V 1990 The scattering transform for the Benjamin-Ono equation Inverse Problems 6 825
    • (1990) Inverse Problems , vol.6 , pp. 825
    • Coifman, R.R.1    Wickerhauser, M.V.2
  • 13
    • 0039436191 scopus 로고
    • On the limit from the intermediate long wave equation to the Benjamin-Ono equation
    • Santini P M, Ablowitz M J and Fokas A S 1984 On the limit from the intermediate long wave equation to the Benjamin-Ono equation J. Math. Phys. 25 892
    • (1984) J. Math. Phys. , vol.25 , pp. 892
    • Santini, P.M.1    Ablowitz, M.J.2    Fokas, A.S.3
  • 14
    • 0038843527 scopus 로고
    • On the Benjamin-Ono equation - Method for exact solution
    • Matsuno Y 1982 On the Benjamin-Ono equation - method for exact solution J. Phys. Soc. Japan 51 3734
    • (1982) J. Phys. Soc. Japan , vol.51 , pp. 3734
    • Matsuno, Y.1
  • 15
    • 0016369301 scopus 로고
    • The inverse scattering transform - Fourier analysis for nonlinear problems
    • Ablowitz M J, Kaup D J, Newell A C and Segur H 1974 The inverse scattering transform - Fourier analysis for nonlinear problems Stud. Appl. Math. 53 249
    • (1974) Stud. Appl. Math. , vol.53 , pp. 249
    • Ablowitz, M.J.1    Kaup, D.J.2    Newell, A.C.3    Segur, H.4
  • 16
    • 0016962049 scopus 로고
    • Closure of the squared Zakharov-Shabat eigenstates
    • Kaup D J 1976 Closure of the squared Zakharov-Shabat eigenstates J. Math. Anal. Appl. 54 849
    • (1976) J. Math. Anal. Appl. , vol.54 , pp. 849
    • Kaup, D.J.1
  • 17
    • 0016971835 scopus 로고
    • A perturbation expansion for the Zakharov-Shabat inverse scattering transform
    • Kaup D J 1976 A perturbation expansion for the Zakharov-Shabat inverse scattering transform SIAM J. Appl. Math. 31 121
    • (1976) SIAM J. Appl. Math. , vol.31 , pp. 121
    • Kaup, D.J.1
  • 18
    • 0041109799 scopus 로고
    • Expansions with respect to squares, symplectic and Poisson structures associated with the Sturm-Liouville problem II
    • Arkad'ev V A, Pogrebkov A K and Polivanov M K 1988 Expansions with respect to squares, symplectic and Poisson structures associated with the Sturm-Liouville problem II Theor. Math. Phys. 75 448
    • (1988) Theor. Math. Phys. , vol.75 , pp. 448
    • Arkad'ev, V.A.1    Pogrebkov, A.K.2    Polivanov, M.K.3
  • 19
    • 0001896758 scopus 로고
    • Quadratic bundle of a general form and nonlinear evolution equations. I. Expansions over 'squared' solutions - The generalized Fourier transforms
    • Gerjikov V S and Ivanov M I 1983 Quadratic bundle of a general form and nonlinear evolution equations. I. Expansions over 'squared' solutions - the generalized Fourier transforms Bulg. J. Phys. 10 13
    • (1983) Bulg. J. Phys. , vol.10 , pp. 13
    • Gerjikov, V.S.1    Ivanov, M.I.2
  • 20
    • 0000347643 scopus 로고
    • Quadratic bundle of a general form and nonlinear evolution equations. II. Hierarchies of the Hamiltonian structures
    • in Russian
    • Gerjikov V S and Ivanov M I 1983 Quadratic bundle of a general form and nonlinear evolution equations. II. Hierarchies of the Hamiltonian structures Bulg. J. Phys. 10 130 (in Russian)
    • (1983) Bulg. J. Phys. , vol.10 , pp. 130
    • Gerjikov, V.S.1    Ivanov, M.I.2
  • 21
    • 0030538778 scopus 로고    scopus 로고
    • Variational method: How it can generate false instabilities
    • Kaup D J and Lakoba T I 1996 Variational method: how it can generate false instabilities J. Math. Phys. 37 308
    • (1996) J. Math. Phys. , vol.37 , pp. 308
    • Kaup, D.J.1    Lakoba, T.I.2
  • 22
    • 0039404425 scopus 로고
    • Hamiltonian structure of the Kadomtsev-Petviashvili-II equation in the class of decreasing Cauchy data
    • Lipovskii V D 1986 Hamiltonian structure of the Kadomtsev-Petviashvili-II equation in the class of decreasing Cauchy data Func. Anal. Appl. 20 282
    • (1986) Func. Anal. Appl. , vol.20 , pp. 282
    • Lipovskii, V.D.1
  • 23
    • 84908734931 scopus 로고
    • Soliton evolution in the presence of perturbations
    • Karpman V I 1979 Soliton evolution in the presence of perturbations Phys. Scr. 20 462
    • (1979) Phys. Scr. , vol.20 , pp. 462
    • Karpman, V.I.1
  • 24
  • 26
    • 0042519302 scopus 로고
    • Investigation of the Hamiltonian structure of the KdV system through r - s matrix formalism revealing some new aspects
    • Kundu A and Basu Mallick B 1990 Investigation of the Hamiltonian structure of the KdV system through r - s matrix formalism revealing some new aspects J. Phys. Soc. Japan 59 1560
    • (1990) J. Phys. Soc. Japan , vol.59 , pp. 1560
    • Kundu, A.1    Basu Mallick, B.2
  • 27
    • 0001062006 scopus 로고
    • The hierarchy of the Benjamin-Ono equation
    • Fokas A S and Fuchssteiner B 1981 The hierarchy of the Benjamin-Ono equation Phys. Lett. 86A 341
    • (1981) Phys. Lett. , vol.86 A , pp. 341
    • Fokas, A.S.1    Fuchssteiner, B.2
  • 28
    • 10944238376 scopus 로고
    • The Benjamin-Ono and related equations
    • Case K M 1981 The Benjamin-Ono and related equations Physica 3D 185
    • (1981) Physica , vol.3 D , pp. 185
    • Case, K.M.1
  • 29
    • 22244466571 scopus 로고
    • Recurrence formula and conserved quantity of the Benjamin-Ono equation
    • Matsuno Y 1983 Recurrence formula and conserved quantity of the Benjamin-Ono equation J. Phys. Soc. Japan 52 2955
    • (1983) J. Phys. Soc. Japan , vol.52 , pp. 2955
    • Matsuno, Y.1
  • 31
    • 0010167489 scopus 로고
    • The soliton perturbation theory based on the Riemann-Hilbert spectral problem
    • Scshesnovich V S 1995 The soliton perturbation theory based on the Riemann-Hilbert spectral problem Chaos, Solitons Fractals 5 2121
    • (1995) Chaos, Solitons Fractals , vol.5 , pp. 2121
    • Scshesnovich, V.S.1
  • 32
    • 22244432026 scopus 로고    scopus 로고
    • PhD Dissertation Clarkson University
    • Lakoba T I 1996 PhD Dissertation Clarkson University
    • (1996)
    • Lakoba, T.I.1
  • 34
    • 0039587886 scopus 로고
    • Recursion operators and bi-Hamiltonian structures in multidimensions. II
    • Fokas A S and Santini P M 1988 Recursion operators and bi-Hamiltonian structures in multidimensions. II Commun. Math. Phys. 116 449
    • (1988) Commun. Math. Phys. , vol.116 , pp. 449
    • Fokas, A.S.1    Santini, P.M.2
  • 35
    • 0012571308 scopus 로고
    • Hamiltonian structure of the Davey-Stewartson equation and Poisson brackets of scattering data
    • Kulish P P and Lipovsky V D 1988 Hamiltonian structure of the Davey-Stewartson equation and Poisson brackets of scattering data Phys. Lett. 127A 413
    • (1988) Phys. Lett. , vol.127 A , pp. 413
    • Kulish, P.P.1    Lipovsky, V.D.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.