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Volumn 38, Issue 3, 2006, Pages 985-1011

Stability of solitary waves of a generalized ostrovsky equation

Author keywords

Solitary waves; Stability; Variational methods

Indexed keywords

CAPILLARY WAVES; KORTEWEG DE VRIES EQUATION; OSTROVSKY EQUATION; VARIATIONAL METHODS;

EID: 34249030634     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/050638722     Document Type: Article
Times cited : (56)

References (26)
  • 1
    • 84894278291 scopus 로고    scopus 로고
    • On the instability of solitary waves solutions of the generalized Benjamin equation
    • J. ANGULO, On the instability of solitary waves solutions of the generalized Benjamin equation, Adv. Differential Equations, 8 (2003), pp. 55-82.
    • (2003) Adv. Differential Equations , vol.8 , pp. 55-82
    • ANGULO, J.1
  • 2
    • 0038523453 scopus 로고
    • On the surface waves in a shallow channel with an uneven bottom
    • E. S. BENILOV, On the surface waves in a shallow channel with an uneven bottom, Stud. Appl. Math., 87 (1992), pp. 1-14.
    • (1992) Stud. Appl. Math , vol.87 , pp. 1-14
    • BENILOV, E.S.1
  • 3
    • 34249063076 scopus 로고    scopus 로고
    • Instability of solitary wave solutions of the 3-dimensional Kadomtsev-Petviashvili equation
    • J. BONA AND Y. LIU, Instability of solitary wave solutions of the 3-dimensional Kadomtsev-Petviashvili equation, Adv. Differential Equations, 7 (2002), pp. 1-23.
    • (2002) Adv. Differential Equations , vol.7 , pp. 1-23
    • BONA, J.1    LIU, Y.2
  • 5
    • 0023648120 scopus 로고
    • Stability and instability of solitary waves of Korteweg-de Vries type
    • J. BONA, P. SOUGANIDIS, AND W. STRAUSS, Stability and instability of solitary waves of Korteweg-de Vries type, Proc. Roy. Soc. London Ser. A, 411 (1987), pp. 395-412.
    • (1987) Proc. Roy. Soc. London Ser. A , vol.411 , pp. 395-412
    • BONA, J.1    SOUGANIDIS, P.2    STRAUSS, W.3
  • 6
    • 0001118971 scopus 로고
    • Stability of Coulomb systems with magnetic fields I. The one-electron atom
    • J. FRÖHLICH, E. H. LIEB, AND M. LOSS, Stability of Coulomb systems with magnetic fields I. The one-electron atom, Comm. Math. Phys., 104 (1986), pp. 251-270.
    • (1986) Comm. Math. Phys , vol.104 , pp. 251-270
    • FRÖHLICH, J.1    LIEB, E.H.2    LOSS, M.3
  • 7
    • 0026364589 scopus 로고
    • On the existence of stationary solitary waves in a rotating field
    • V. N. GALKIN AND Y. A. STEPANYANTS, On the existence of stationary solitary waves in a rotating field, J. Appl. Math. Mech., 55 (1991), pp. 939-943.
    • (1991) J. Appl. Math. Mech , vol.55 , pp. 939-943
    • GALKIN, V.N.1    STEPANYANTS, Y.A.2
  • 8
    • 0043038583 scopus 로고
    • Approximate and numerical solutions of the stationary Ostrovsky equation
    • O. A. GILMAN, R. GRIMSHAW, AND Y. A. STEPANYANTS, Approximate and numerical solutions of the stationary Ostrovsky equation, Stud. Appl. Math., 95 (1995), pp. 115-126.
    • (1995) Stud. Appl. Math , vol.95 , pp. 115-126
    • GILMAN, O.A.1    GRIMSHAW, R.2    STEPANYANTS, Y.A.3
  • 9
    • 0022107866 scopus 로고
    • Evolution equations for weakly nonlinear long internal waves in a rotating fluid
    • R. GRIMSHAW, Evolution equations for weakly nonlinear long internal waves in a rotating fluid, Stud. Appl. Math., 73 (1985), pp. 1-33.
    • (1985) Stud. Appl. Math , vol.73 , pp. 1-33
    • GRIMSHAW, R.1
  • 10
    • 34249011244 scopus 로고    scopus 로고
    • J. GONÇALVES RIBEIRO, Instability of symmetric stationary states for some nonlinear Schrödinger equations with an external magnetic field, Ann. Inst. H. Poincaré, Phys. Théor., 54 (1991), pp. 403-433.
    • J. GONÇALVES RIBEIRO, Instability of symmetric stationary states for some nonlinear Schrödinger equations with an external magnetic field, Ann. Inst. H. Poincaré, Phys. Théor., 54 (1991), pp. 403-433.
  • 11
    • 0001307126 scopus 로고    scopus 로고
    • Existence and stability of Camm type steady states in galactic dynamics
    • Y. GUO AND G. REIN, Existence and stability of Camm type steady states in galactic dynamics, Indiana U. Math. J., 48 (1999), pp. 1237-1255.
    • (1999) Indiana U. Math. J , vol.48 , pp. 1237-1255
    • GUO, Y.1    REIN, G.2
  • 12
    • 0000262859 scopus 로고
    • On the stability of solitary waves in weakly dispersive media
    • B. B. KADOMTSEV AND V. I. PETVIASHVILI, On the stability of solitary waves in weakly dispersive media, Sov. Phys. Dokl., 15 (1970), pp. 539-541.
    • (1970) Sov. Phys. Dokl , vol.15 , pp. 539-541
    • KADOMTSEV, B.B.1    PETVIASHVILI, V.I.2
  • 13
    • 84989056623 scopus 로고
    • The effect of the earth's rotation on the propagation of weak nonlinear surface and internal long oceanic waves
    • A. LEONOV, The effect of the earth's rotation on the propagation of weak nonlinear surface and internal long oceanic waves, Ann. New York Acad. Sci., 373 (1981), pp. 150-159.
    • (1981) Ann. New York Acad. Sci , vol.373 , pp. 150-159
    • LEONOV, A.1
  • 14
    • 0001043191 scopus 로고    scopus 로고
    • A stability analysis of fifth-order water wave models
    • S. LEVANDOSKY, A stability analysis of fifth-order water wave models, Phys. D, 125 (1999). pp. 222-240.
    • (1999) Phys. D , vol.125 , pp. 222-240
    • LEVANDOSKY, S.1
  • 16
    • 85030707196 scopus 로고
    • The concentration-compactness principle in the calculus of variations. The locally compact case, Part 1 and Part 2
    • P. L. LIONS, The concentration-compactness principle in the calculus of variations. The locally compact case, Part 1 and Part 2, Ann. Inst. H. Poincaré, Anal. Non Linéaire, 1 (1984), pp. 109-145; 223-283.
    • (1984) Ann. Inst. H. Poincaré, Anal. Non Linéaire , vol.1
    • LIONS, P.L.1
  • 18
    • 3042638045 scopus 로고    scopus 로고
    • Stability of solitary waves and weak rotation limit for the Ostrovsky equation
    • Y. LIU AND V. VARLAMOV, Stability of solitary waves and weak rotation limit for the Ostrovsky equation, J. Differential Equations, 203 (2004), pp. 159-183.
    • (2004) J. Differential Equations , vol.203 , pp. 159-183
    • LIU, Y.1    VARLAMOV, V.2
  • 19
    • 33748069497 scopus 로고
    • Korteweg-de Vries equation and generalizations II. Existence conservation laws and constant of motion
    • R. M. MIURA, C. S. GARDNER, AND M. D. KRUSKAL, Korteweg-de Vries equation and generalizations II. Existence conservation laws and constant of motion, J. Math. Phys., 9 (1968), pp. 1204-1209.
    • (1968) J. Math. Phys , vol.9 , pp. 1204-1209
    • MIURA, R.M.1    GARDNER, C.S.2    KRUSKAL, M.D.3
  • 20
    • 0000401372 scopus 로고
    • Nonlinear internal waves in a rotating ocean
    • L. A. OSTROVSKY, Nonlinear internal waves in a rotating ocean, Okeanologia, 18 (1978), pp. 181-191.
    • (1978) Okeanologia , vol.18 , pp. 181-191
    • OSTROVSKY, L.A.1
  • 21
    • 34249000837 scopus 로고    scopus 로고
    • L. A. OSTROVSKY AND Y. A. STEPANYANTS, Nonlinear surface and internal waves in rotating fluids, in Nonlinear Waves 3, Res. Rep. Phys., Springer, Berlin, Heidelberg, 1990, pp. 106-128.
    • L. A. OSTROVSKY AND Y. A. STEPANYANTS, Nonlinear surface and internal waves in rotating fluids, in Nonlinear Waves 3, Res. Rep. Phys., Springer, Berlin, Heidelberg, 1990, pp. 106-128.
  • 24
    • 0000229397 scopus 로고
    • Stable standing waves of nonlinear Klein-Gordon equations
    • J. SHATAH, Stable standing waves of nonlinear Klein-Gordon equations, Comm. Math. Phys., 91 (1983), pp. 313-327.
    • (1983) Comm. Math. Phys , vol.91 , pp. 313-327
    • SHATAH, J.1
  • 25
    • 0001420204 scopus 로고
    • Instability of nonlinear bound states
    • J. SHATAH AND W. STRAUSS, Instability of nonlinear bound states, Comm. Math. Phys., 100 (1985), pp. 173-190.
    • (1985) Comm. Math. Phys , vol.100 , pp. 173-190
    • SHATAH, J.1    STRAUSS, W.2
  • 26
    • 1042290983 scopus 로고    scopus 로고
    • Cauchy problem for the Ostrovsky equation
    • V. VARLAMOV AND Y. LIU, Cauchy problem for the Ostrovsky equation, Discrete Contin. Dyn. Syst., 10 (2004), pp. 731-753.
    • (2004) Discrete Contin. Dyn. Syst , vol.10 , pp. 731-753
    • VARLAMOV, V.1    LIU, Y.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.