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Volumn , Issue 47, 2003, Pages 2529-2564

The Zero-dispersion Limit for the Odd Flows in the Focusing Zakharov-shabat Hierarchy

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EID: 0345059972     PISSN: 10737928     EISSN: None     Source Type: Journal    
DOI: 10.1155/s1073792803130851     Document Type: Article
Times cited : (16)

References (24)
  • 1
    • 0030263239 scopus 로고    scopus 로고
    • Semiclassical eigenvalue distribution of the Zakharov-Shabat eigenvalue problem
    • J. C. Bronski, Semiclassical eigenvalue distribution of the Zakharov-Shabat eigenvalue problem, Phys. D 97 (1996), no. 4, 376-397.
    • (1996) Phys. D , vol.97 , Issue.4 , pp. 376-397
    • Bronski, J.C.1
  • 2
    • 0031540140 scopus 로고    scopus 로고
    • The behavior of the Weyl function in the zero-dispersion KdV limit
    • N. M. Ercolani, C. D. Levermore, and T. Zhang, The behavior of the Weyl function in the zero-dispersion KdV limit, Comm. Math. Phys. 183 (1997), no. 1, 119-143.
    • (1997) Comm. Math. Phys. , vol.183 , Issue.1 , pp. 119-143
    • Ercolani, N.M.1    Levermore, C.D.2    Zhang, T.3
  • 3
    • 84980178052 scopus 로고
    • Multiphase averaging and the inverse spectral solution of the Korteweg-de Vries equation
    • H. Flaschka, M. G. Forest, and D. W. McLaughlin, Multiphase averaging and the inverse spectral solution of the Korteweg-de Vries equation, Comm. Pure Appl. Math. 33 (1980), no. 6, 739-784.
    • (1980) Comm. Pure Appl. Math. , vol.33 , Issue.6 , pp. 739-784
    • Flaschka, H.1    Forest, M.G.2    McLaughlin, D.W.3
  • 5
    • 0002412295 scopus 로고
    • Geometry and modulation theory for the periodic nonlinear Schrödinger equation
    • Oscillation Theory, Computation, and Methods of Compensated Compactness (Minneapolis, Minn, 1985) (C. Dafermos, J. L. Ericksen, D. Kinderlehrer, and M. Slemrod, eds.), Springer-Verlag, New York
    • M. G. Forest and J.-E. Lee, Geometry and modulation theory for the periodic nonlinear Schrödinger equation, Oscillation Theory, Computation, and Methods of Compensated Compactness (Minneapolis, Minn, 1985) (C. Dafermos, J. L. Ericksen, D. Kinderlehrer, and M. Slemrod, eds.), the IMA Volumes in Mathematics and Its Applications, vol. 2, Springer-Verlag, New York, 1986, pp. 35-69.
    • (1986) The IMA Volumes in Mathematics and Its Applications , vol.2 , pp. 35-69
    • Forest, M.G.1    Lee, J.-E.2
  • 6
    • 36049057587 scopus 로고
    • Method for solving the Korteweg-de Vries equation
    • G. S. Gardner, J. M. Greene, M. D. Kruskal, and R. M. Miura, Method for solving the Korteweg-de Vries equation, Phys. Rev. Lett. 19 (1967), no. 19, 1095-1097.
    • (1967) Phys. Rev. Lett. , vol.19 , Issue.19 , pp. 1095-1097
    • Gardner, G.S.1    Greene, J.M.2    Kruskal, M.D.3    Miura, R.M.4
  • 7
    • 0000953038 scopus 로고
    • The behavior of solutions of the NLS equation in the semiclassical limit
    • Singular Limits of Dispersive Waves (Lyon, 1991) (N. M. Ercolani, I. R. Gabitov, C. D. Levermore, and D. Serre, eds.), Plenum, New York
    • S. Jin, C. D. Levermore, and D. W. McLaughlin, The behavior of solutions of the NLS equation in the semiclassical limit, Singular Limits of Dispersive Waves (Lyon, 1991) (N. M. Ercolani, I. R. Gabitov, C. D. Levermore, and D. Serre, eds.), NATO Adv. Sci. Inst. Ser. B Phys., vol. 320, Plenum, New York, 1994, pp. 235-255.
    • (1994) NATO Adv. Sci. Inst. Ser. B Phys. , vol.320 , pp. 235-255
    • Jin, S.1    Levermore, C.D.2    McLaughlin, D.W.3
  • 8
    • 0033438093 scopus 로고    scopus 로고
    • The semiclassical limit of the defocusing NLS hierarchy
    • _, The semiclassical limit of the defocusing NLS hierarchy, Comm. Pure Appl. Math. 52 (1999), no. 5, 613-654.
    • (1999) Comm. Pure Appl. Math. , vol.52 , Issue.5 , pp. 613-654
  • 9
    • 85009055469 scopus 로고    scopus 로고
    • Semiclassical Soliton Ensembles for the Focusing Nonlinear Schrödinger Equation
    • Princeton University Press, Princeton
    • S. Kamvissis, K. D. T.-R. McLaughlin, and P. D. Miller, Semiclassical Soliton Ensembles for the Focusing Nonlinear Schrödinger Equation, Annals of Mathematics Studies, Princeton University Press, Princeton, 2003.
    • (2003) Annals of Mathematics Studies
    • Kamvissis, S.1    McLaughlin, K.D.T.-R.2    Miller, P.D.3
  • 10
    • 41349122386 scopus 로고    scopus 로고
    • Purely imaginary eigenvalues of Zakharov-Shabat systems
    • 036607
    • M. Klaus and J. K. Shaw, Purely imaginary eigenvalues of Zakharov-Shabat systems, Phys. Rev. E (3) 65 (2002), no. 3, 036607, 1-5.
    • (2002) Phys. Rev. E (3) , vol.65 , Issue.3 , pp. 1-5
    • Klaus, M.1    Shaw, J.K.2
  • 11
    • 0037881760 scopus 로고    scopus 로고
    • Linear Algebra
    • John Wiley & Sons, New York
    • P. D. Lax, Linear Algebra, Pure and Applied Mathematics, John Wiley & Sons, New York, 1997.
    • (1997) Pure and Applied Mathematics
    • Lax, P.D.1
  • 12
    • 0040641385 scopus 로고
    • The zero dispersion limit for the Korteweg-de Vries KdV equation
    • P. D. Lax and C. D. Levermore, The zero dispersion limit for the Korteweg-de Vries KdV equation, Proc. Nat. Acad. Sci. U.S.A. 76 (1979), no. 8, 3602-3606.
    • (1979) Proc. Nat. Acad. Sci. U.S.A. , vol.76 , Issue.8 , pp. 3602-3606
    • Lax, P.D.1    Levermore, C.D.2
  • 13
    • 84990575581 scopus 로고
    • The small dispersion limit of the Korteweg-de Vries equation.I
    • _, The small dispersion limit of the Korteweg-de Vries equation. I, Comm. Pure Appl. Math. 36 (1983), no. 3, 253-290.
    • (1983) Comm. Pure Appl. Math. , vol.36 , Issue.3 , pp. 253-290
  • 14
    • 84990602637 scopus 로고
    • The small dispersion limit of the Korteweg-de Vries equation. II
    • _, The small dispersion limit of the Korteweg-de Vries equation. II, Comm. Pure Appl. Math. 36 (1983), no. 5, 571-593.
    • (1983) Comm. Pure Appl. Math. , vol.36 , Issue.5 , pp. 571-593
  • 15
    • 84990587869 scopus 로고
    • The small dispersion limit of the Korteweg-de Vries equation. III
    • _, The small dispersion limit of the Korteweg-de Vries equation. III, Comm. Pure Appl. Math. 36 (1983), no. 6, 809-829.
    • (1983) Comm. Pure Appl. Math. , vol.36 , Issue.6 , pp. 809-829
  • 16
    • 0012009827 scopus 로고
    • The generation and propagation of oscillations in dispersive initial value problems and their limiting behavior
    • (A. S. Fokas and V. E. Zakharov, eds.), Springer Ser. Nonlinear Dynam., Springer, Berlin
    • P. D. Lax, C. D. Levermore, and S. Venakides, The generation and propagation of oscillations in dispersive initial value problems and their limiting behavior, Important Developments in Soliton Theory (A. S. Fokas and V. E. Zakharov, eds.), Springer Ser. Nonlinear Dynam., Springer, Berlin, 1993, pp. 205-241.
    • (1993) Important Developments in Soliton Theory , pp. 205-241
    • Lax, P.D.1    Levermore, C.D.2    Venakides, S.3
  • 17
    • 0040325515 scopus 로고    scopus 로고
    • The KdV zero-dispersion limit and densities of Dirichlet spectra
    • Recent Advances in Partial Differential Equations, Venice 1996. Proceedings of the Conference in Honor of the 70th Birthdays of Peter D. Lax and Louis Nirenberg (R. Spigler and S. Venakides, eds.), American Mathematical Society, Rhode Island
    • C. D. Levermore, The KdV zero-dispersion limit and densities of Dirichlet spectra, Recent Advances in Partial Differential Equations, Venice 1996. Proceedings of the Conference in Honor of the 70th Birthdays of Peter D. Lax and Louis Nirenberg (R. Spigler and S. Venakides, eds.), Proc. Sympos. Appl. Math., vol. 54, American Mathematical Society, Rhode Island, 1998, pp. 187-210.
    • (1998) Proc. Sympos. Appl. Math. , vol.54 , pp. 187-210
    • Levermore, C.D.1
  • 18
    • 36849110505 scopus 로고
    • Korteweg-de Vries equation and generalizations.I. A remarkable explicit nonlinear transformation
    • R. M. Miura, Korteweg-de Vries equation and generalizations. I. A remarkable explicit nonlinear transformation, J. Mathematical Phys. 9 (1968), 1202-1204.
    • (1968) J. Mathematical Phys. , vol.9 , pp. 1202-1204
    • Miura, R.M.1
  • 19
    • 84990614472 scopus 로고
    • The generation of modulated wavetrains in the solution of the Korteweg-de Vries equation
    • S. Venakides, The generation of modulated wavetrains in the solution of the Korteweg-de Vries equation, Comm. Pure Appl. Math. 38 (1985), no. 6, 883-909.
    • (1985) Comm. Pure Appl. Math. , vol.38 , Issue.6 , pp. 883-909
    • Venakides, S.1
  • 20
    • 84967712805 scopus 로고
    • The zero dispersion limit of the Korteweg-de Vries equation with periodic initial data
    • _, The zero dispersion limit of the Korteweg-de Vries equation with periodic initial data, Trans. Amer. Math. Soc. 301 (1987), no. 1, 189-226.
    • (1987) Trans. Amer. Math. Soc. , vol.301 , Issue.1 , pp. 189-226
  • 21
    • 84990586440 scopus 로고
    • The Korteweg-de Vries equation with small dispersion: Higher order Lax-levermore theory
    • _, The Korteweg-de Vries equation with small dispersion: higher order Lax-Levermore theory, Comm. Pure Appl. Math. 43 (1990), no. 3, 335-361.
    • (1990) Comm. Pure Appl. Math. , vol.43 , Issue.3 , pp. 335-361
  • 22
    • 0001273346 scopus 로고
    • Non-linear dispersive waves
    • G. B. Whitham, Non-linear dispersive waves, Proc. Roy. Soc. Ser. A 283 (1965), 238-261.
    • (1965) Proc. Roy. Soc. Ser. A , vol.283 , pp. 238-261
    • Whitham, G.B.1
  • 23
    • 0002557939 scopus 로고
    • Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media
    • V. E. Zakharov and A. B. Shabat, Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media, Soviet Phys. JETP 34 (1972), no. 1, 62-69.
    • (1972) Soviet Phys. JETP , vol.34 , Issue.1 , pp. 62-69
    • Zakharov, V.E.1    Shabat, A.B.2
  • 24
    • 0000169358 scopus 로고
    • Interaction between solitons ina stable medium
    • _, Interaction between solitons in a stable medium, Soviet Phys. JETP 37 (1973), 823-828.
    • (1973) Soviet Phys. JETP , vol.37 , pp. 823-828


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