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Volumn 236, Issue 1, 2007, Pages 199-236

Uniqueness properties of higher order dispersive equations

Author keywords

Higher order dispersive models; Uniqueness properties

Indexed keywords


EID: 33947610773     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1016/j.jde.2007.01.015     Document Type: Article
Times cited : (18)

References (39)
  • 1
    • 0017452470 scopus 로고
    • A general theory for interactions between short and long waves
    • Benney D.J. A general theory for interactions between short and long waves. Stud. Appl. Math. 56 1 (1977) 81-94
    • (1977) Stud. Appl. Math. , vol.56 , Issue.1 , pp. 81-94
    • Benney, D.J.1
  • 2
    • 0001923237 scopus 로고
    • Au delà des opérateurs pseudo-différentiels
    • Société Mathématique de France, Paris
    • Coifman R.R., and Meyer Y. Au delà des opérateurs pseudo-différentiels. Astérisque vol. 57 (1978), Société Mathématique de France, Paris
    • (1978) Astérisque , vol.57
    • Coifman, R.R.1    Meyer, Y.2
  • 3
    • 84968508844 scopus 로고
    • Local smoothing properties of dispersive equations
    • Constantin P., and Saut J.-C. Local smoothing properties of dispersive equations. J. Amer. Math. Soc. 1 2 (1988) 413-439
    • (1988) J. Amer. Math. Soc. , vol.1 , Issue.2 , pp. 413-439
    • Constantin, P.1    Saut, J.-C.2
  • 4
    • 14844335660 scopus 로고    scopus 로고
    • Strichartz estimates for dispersive equations and solvability of the Kawahara equation
    • Cui S., and Tao S. Strichartz estimates for dispersive equations and solvability of the Kawahara equation. J. Math. Anal. Appl. 304 2 (2005) 683-702
    • (2005) J. Math. Anal. Appl. , vol.304 , Issue.2 , pp. 683-702
    • Cui, S.1    Tao, S.2
  • 5
    • 33846785117 scopus 로고    scopus 로고
    • On uniqueness properties of solutions of the k-generalized KdV equations
    • Escauriaza L., Kenig C., Ponce G., and Vega L. On uniqueness properties of solutions of the k-generalized KdV equations. J. Funct. Anal. 244 (2007) 504-535
    • (2007) J. Funct. Anal. , vol.244 , pp. 504-535
    • Escauriaza, L.1    Kenig, C.2    Ponce, G.3    Vega, L.4
  • 6
    • 36049057587 scopus 로고
    • Method for solving the Korteweg-de Vries equation
    • Gardner C., Greene J., Kruskal M., and Miura R. Method for solving the Korteweg-de Vries equation. Phys. Rev. Lett. 19 (1967) 1095-1097
    • (1967) Phys. Rev. Lett. , vol.19 , pp. 1095-1097
    • Gardner, C.1    Greene, J.2    Kruskal, M.3    Miura, R.4
  • 7
    • 84980193643 scopus 로고
    • Korteweg-de Vries equation and generalization. VI. Methods for exact solution
    • Gardner C.S., Greene J.M., Kruskal M.D., and Miura R.M. Korteweg-de Vries equation and generalization. VI. Methods for exact solution. Comm. Pure Appl. Math. 27 (1974) 97-133
    • (1974) Comm. Pure Appl. Math. , vol.27 , pp. 97-133
    • Gardner, C.S.1    Greene, J.M.2    Kruskal, M.D.3    Miura, R.M.4
  • 9
    • 38249000245 scopus 로고
    • Carleman type estimates in an anisotropic case and applications
    • Isakov V. Carleman type estimates in an anisotropic case and applications. J. Differential Equations 105 2 (1993) 217-238
    • (1993) J. Differential Equations , vol.105 , Issue.2 , pp. 217-238
    • Isakov, V.1
  • 10
    • 0000985657 scopus 로고
    • Weak non-linear hydromagnetic waves in a cold collision-free plasma
    • Kakutani T., and Ono H. Weak non-linear hydromagnetic waves in a cold collision-free plasma. J. Phys. Soc. Japan 5 (1969) 1305-1318
    • (1969) J. Phys. Soc. Japan , vol.5 , pp. 1305-1318
    • Kakutani, T.1    Ono, H.2
  • 11
    • 0002362136 scopus 로고
    • On the Cauchy problem for the (generalized) Korteweg-de Vries equation
    • Studies in Applied Mathematics, Academic Press, New York
    • Kato T. On the Cauchy problem for the (generalized) Korteweg-de Vries equation. Studies in Applied Mathematics. Adv. Math. Suppl. Stud. vol. 8 (1983), Academic Press, New York 93-128
    • (1983) Adv. Math. Suppl. Stud. , vol.8 , pp. 93-128
    • Kato, T.1
  • 12
    • 0002408905 scopus 로고
    • x + 6 R ψ = λ ψ
    • x + 6 R ψ = λ ψ. Stud. Appl. Math. 62 3 (1980) 189-216
    • (1980) Stud. Appl. Math. , vol.62 , Issue.3 , pp. 189-216
    • Kaup, D.J.1
  • 13
    • 77952762814 scopus 로고
    • Oscillatory solitary waves in dispersive media
    • Kawahara T. 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
    • 84972580144 scopus 로고
    • On the (generalized) Korteweg-de Vries equation
    • Kenig C.E., Ponce G., and Vega L. On the (generalized) Korteweg-de Vries equation. Duke Math. J. 59 3 (1989) 585-610
    • (1989) Duke Math. J. , vol.59 , Issue.3 , pp. 585-610
    • Kenig, C.E.1    Ponce, G.2    Vega, L.3
  • 15
    • 0001969794 scopus 로고
    • Oscillatory integrals and regularity of dispersive equations
    • Kenig C.E., Ponce G., and Vega L. Oscillatory integrals and regularity of dispersive equations. Indiana Univ. Math. J. 40 1 (1991) 33-69
    • (1991) Indiana Univ. Math. J. , vol.40 , Issue.1 , pp. 33-69
    • Kenig, C.E.1    Ponce, G.2    Vega, L.3
  • 16
    • 84966204722 scopus 로고
    • Higher-order nonlinear dispersive equations
    • Kenig C.E., Ponce G., and Vega L. Higher-order nonlinear dispersive equations. Proc. Amer. Math. Soc. 122 1 (1994) 157-166
    • (1994) Proc. Amer. Math. Soc. , vol.122 , Issue.1 , pp. 157-166
    • Kenig, C.E.1    Ponce, G.2    Vega, L.3
  • 18
    • 0742323752 scopus 로고    scopus 로고
    • On the unique continuation of solutions to the generalized KdV equation
    • Kenig C.E., Ponce G., and Vega L. On the unique continuation of solutions to the generalized KdV equation. Math. Res. Lett. 10 5-6 (2003) 833-846
    • (2003) Math. Res. Lett. , vol.10 , Issue.5-6 , pp. 833-846
    • Kenig, C.E.1    Ponce, G.2    Vega, L.3
  • 19
    • 0000106540 scopus 로고
    • Existence and nonexistence of solitary wave solutions to higher-order model evolution equations
    • Kichenassamy S., and Olver P.J. Existence and nonexistence of solitary wave solutions to higher-order model evolution equations. SIAM J. Math. Anal. 23 5 (1992) 1141-1166
    • (1992) SIAM J. Math. Anal. , vol.23 , Issue.5 , pp. 1141-1166
    • Kichenassamy, S.1    Olver, P.J.2
  • 20
    • 0001524186 scopus 로고
    • On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary wave
    • Korteweg D., and de Vries G. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary wave. Philos. Mag. 39 (1895) 422-443
    • (1895) Philos. Mag. , vol.39 , pp. 422-443
    • Korteweg, D.1    de Vries, G.2
  • 21
    • 0031481541 scopus 로고    scopus 로고
    • The role of the Korteweg-de Vries hierarchy in the N-soliton dynamics of the shallow water wave equation
    • Kraenkel R.A., Manna M.A., Montero J.C., and Pereira J.G. The role of the Korteweg-de Vries hierarchy in the N-soliton dynamics of the shallow water wave equation. J. Phys. Soc. Japan 66 5 (1997) 1277-1281
    • (1997) J. Phys. Soc. Japan , vol.66 , Issue.5 , pp. 1277-1281
    • Kraenkel, R.A.1    Manna, M.A.2    Montero, J.C.3    Pereira, J.G.4
  • 22
    • 21844521262 scopus 로고
    • The Korteweg-de Vries hierarchy and long water-waves
    • Kraenkel R.A., Manna M.A., and Pereira J.G. The Korteweg-de Vries hierarchy and long water-waves. J. Math. Phys. 36 1 (1995) 307-320
    • (1995) J. Math. Phys. , vol.36 , Issue.1 , pp. 307-320
    • Kraenkel, R.A.1    Manna, M.A.2    Pereira, J.G.3
  • 23
    • 0005544461 scopus 로고
    • The reductive perturbation method and the Korteweg-de Vries hierarchy
    • Kraenkel R.A., Pereira J.G., and Manna M.A. The reductive perturbation method and the Korteweg-de Vries hierarchy. Acta Appl. Math. 39 1-3 (1995) 389-403
    • (1995) Acta Appl. Math. , vol.39 , Issue.1-3 , pp. 389-403
    • Kraenkel, R.A.1    Pereira, J.G.2    Manna, M.A.3
  • 24
    • 84956276540 scopus 로고
    • Generalized solutions of the Cauchy problem for the Korteweg-de Vries equation
    • Kruzhkov S., and Faminskii A. Generalized solutions of the Cauchy problem for the Korteweg-de Vries equation. Math. USSR Sb. 48 (1984) 93-138
    • (1984) Math. USSR Sb. , vol.48 , pp. 93-138
    • Kruzhkov, S.1    Faminskii, A.2
  • 25
    • 84981754671 scopus 로고
    • Integrals of nonlinear equations of evolution and solitary waves
    • Lax P.D. 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.D.1
  • 26
    • 0000991407 scopus 로고
    • Almost periodic solutions of the KdV equation
    • Lax P.D. Almost periodic solutions of the KdV equation. SIAM Rev. 18 3 (1976) 351-375
    • (1976) SIAM Rev. , vol.18 , Issue.3 , pp. 351-375
    • Lax, P.D.1
  • 27
    • 0007283021 scopus 로고
    • Comments on the use of the Korteweg-de Vries equation in the study of anharmonic lattices
    • Lisher E. Comments on the use of the Korteweg-de Vries equation in the study of anharmonic lattices. Proc. R. Soc. Lond. Ser. A 339 (1974) 119-126
    • (1974) Proc. R. Soc. Lond. Ser. A , vol.339 , pp. 119-126
    • Lisher, E.1
  • 28
    • 38249001362 scopus 로고
    • Lax pairs and higher order models for water waves
    • Ponce G. Lax pairs and higher order models for water waves. J. Differential Equations 102 2 (1993) 360-381
    • (1993) J. Differential Equations , vol.102 , Issue.2 , pp. 360-381
    • Ponce, G.1
  • 29
    • 0001533070 scopus 로고
    • Quelques généralisations de l'équation de Korteweg-de Vries. II
    • Saut J.-C. Quelques généralisations de l'équation de Korteweg-de Vries. II. J. Differential Equations 33 3 (1979) 320-335
    • (1979) J. Differential Equations , vol.33 , Issue.3 , pp. 320-335
    • Saut, J.-C.1
  • 30
    • 0000523343 scopus 로고
    • Unique continuation for some evolution equations
    • Saut J.-C., and Scheurer B. Unique continuation for some evolution equations. J. Differential Equations 66 1 (1987) 118-139
    • (1987) J. Differential Equations , vol.66 , Issue.1 , pp. 118-139
    • Saut, J.-C.1    Scheurer, B.2
  • 31
    • 0001395372 scopus 로고
    • A method for finding N-soliton solutions of the KdV equation and KdV-like equation
    • Sawada K., and Kotera T. A method for finding N-soliton solutions of the KdV equation 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
  • 32
    • 0009394470 scopus 로고
    • The initial value problem for the sequence of generalized Korteweg-de Vries equations
    • Schwarz Jr. M. The initial value problem for the sequence of generalized Korteweg-de Vries equations. Adv. Math. 54 1 (1984) 22-56
    • (1984) Adv. Math. , vol.54 , Issue.1 , pp. 22-56
    • Schwarz Jr., M.1
  • 33
    • 0007076395 scopus 로고
    • On the long time behaviour of a generalized KdV equation
    • Sidi A., Sulem C., and Sulem P.-L. On the long time behaviour of a generalized KdV equation. Acta Appl. Math. 7 1 (1986) 35-47
    • (1986) Acta Appl. Math. , vol.7 , Issue.1 , pp. 35-47
    • Sidi, A.1    Sulem, C.2    Sulem, P.-L.3
  • 34
    • 0001679726 scopus 로고
    • Regularity of solutions to the Schrödinger equation
    • Sjölin P. Regularity of solutions to the Schrödinger equation. Duke Math. J. 55 3 (1987) 699-715
    • (1987) Duke Math. J. , vol.55 , Issue.3 , pp. 699-715
    • Sjölin, P.1
  • 35
    • 84972553620 scopus 로고
    • Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations
    • Strichartz R.S. Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations. Duke Math. J. 44 3 (1977) 705-714
    • (1977) Duke Math. J. , vol.44 , Issue.3 , pp. 705-714
    • Strichartz, R.S.1
  • 36
    • 6344270318 scopus 로고    scopus 로고
    • Analyticity of solutions of the Korteweg-de Vries equation
    • Tarama S. Analyticity of solutions of the Korteweg-de Vries equation. J. Math. Kyoto Univ. 44 1 (2004) 1-32
    • (2004) J. Math. Kyoto Univ. , vol.44 , Issue.1 , pp. 1-32
    • Tarama, S.1
  • 37
    • 0000801121 scopus 로고
    • Schrödinger equations: Pointwise convergence to the initial data
    • Vega L. Schrödinger equations: Pointwise convergence to the initial data. Proc. Amer. Math. Soc. 102 4 (1988) 874-878
    • (1988) Proc. Amer. Math. Soc. , vol.102 , Issue.4 , pp. 874-878
    • Vega, L.1
  • 38
    • 0005748256 scopus 로고
    • Unique continuation for the Korteweg-de Vries equation
    • Zhang B.Y. Unique continuation for the Korteweg-de Vries equation. SIAM J. Math. Anal. 23 1 (1992) 55-71
    • (1992) SIAM J. Math. Anal. , vol.23 , Issue.1 , pp. 55-71
    • Zhang, B.Y.1
  • 39
    • 0023455218 scopus 로고
    • Symmetry breaking in periodic and solitary gravity-capillary waves on water of finite depth
    • Zufiria J. Symmetry breaking in periodic and solitary gravity-capillary waves on water of finite depth. J. Fluid Mech. 184 (1987) 183-206
    • (1987) J. Fluid Mech. , vol.184 , pp. 183-206
    • Zufiria, J.1


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