The Whitham-type equations and linear overdetermined systems of Euler-Poisson-Darboux type
Fei Ran Tian
Source: Duke Math. J. Volume 74, Number 1
(1994), 203-221.
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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077288016
Mathematical Reviews number (MathSciNet): MR1271470
Zentralblatt MATH identifier: 0826.35092
Digital Object Identifier: doi:10.1215/S0012-7094-94-07410-3
References
[1] B. A. Dubrovin and S. P. Novikov, The Hamiltonian formalism of one-dimensional systems of hydrodynamic type and Bogolyubov-Whitham averaging method, Soviet Math. Dokl. 27 (1983), 665–669.
Zentralblatt MATH: 0553.35011
Mathematical Reviews (MathSciNet): MR715332
[2] B. A. Dubrovin and S. P. Novikov, Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory, Russian Math. Surveys 44 (1989), no. 6, 35–124.
Zentralblatt MATH: 0712.58032
Mathematical Reviews (MathSciNet): MR1037010
[3] 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.
Mathematical Reviews (MathSciNet): MR81k:35142
Zentralblatt MATH: 0454.35080
Digital Object Identifier: doi:10.1002/cpa.3160330605
[4] I. M. Krichever, The method of averaging for two-dimensional “integrable” equations, Funct. Anal. Appl. 22 (1988), 200–213.
Mathematical Reviews (MathSciNet): MR961760
[5] V. R. Kudashev and S. E. Sharapov, The inheritance of $KdV$ symmetries under Whitham averaging and hydrodynamic symmetries of the Whitham equations, Theoret. and Math. Phys. 87 (1991), 358–363.
Zentralblatt MATH: 0736.76008
Mathematical Reviews (MathSciNet): MR1122778
[6] V. R. Kudashev, “Waves-number conservation” and succession of symmetries during a Whitham averaging, JETP 54 (1991), 175–178.
[7] P. D. Lax, Hyperbolic systems of conservation laws and the mathematical theory of shock waves, Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1973.
Mathematical Reviews (MathSciNet): MR50:2709
Zentralblatt MATH: 0268.35062
[8]1 P. D. Lax and C. D. Levermore, The small dispersion limit of the Korteweg-de Vries equation. I, Comm. Pure Appl. Math. 36 (1983), no. 3, 253–290.
Mathematical Reviews (MathSciNet): MR85g:35105a
Zentralblatt MATH: 0532.35067
Digital Object Identifier: doi:10.1002/cpa.3160360302
[8]2 P. D. Lax and C. D. Levermore, The small dispersion limit of the Korteweg-de Vries equation. II, Comm. Pure Appl. Math. 36 (1983), no. 5, 571–593.
Mathematical Reviews (MathSciNet): MR85g:35105b
Zentralblatt MATH: 0527.35073
Digital Object Identifier: doi:10.1002/cpa.3160360503
[8]3 P. D. Lax and C. D. Levermore, The small dispersion limit of the Korteweg-de Vries equation. III, Comm. Pure Appl. Math. 36 (1983), no. 6, 809–829.
Mathematical Reviews (MathSciNet): MR85g:35105c
Zentralblatt MATH: 0527.35074
Digital Object Identifier: doi:10.1002/cpa.3160360606
[9] C. D. Levermore, The hyperbolic nature of the zero dispersion KdV limit, Comm. Partial Differential Equations 13 (1988), no. 4, 495–514.
Mathematical Reviews (MathSciNet): MR89h:35302
Zentralblatt MATH: 0678.35081
Digital Object Identifier: doi:10.1080/03605308808820550
[10] F. R. Tian, Oscillations of the zero dispersion limit of the Korteweg-de Vries equation, Ph.D. dissertation, New York University, 1991.
[11] F. R. Tian, Oscillations of the zero dispersion limit of the Korteweg-de Vries equation, Comm. Pure Appl. Math. 46 (1993), no. 8, 1093–1129.
Mathematical Reviews (MathSciNet): MR94h:35234
Zentralblatt MATH: 0810.35114
Digital Object Identifier: doi:10.1002/cpa.3160460802
[12] Fei Ran Tian, On the initial value problem of the Whitham averaged system, Singular limits of dispersive waves (Lyon, 1991) eds. N. Ercolani, T. Gabitov, D. Levermore, and D. Serre, NATO Adv. Sci. Inst. Ser. B Phys., vol. 320, Plenum, New York, 1994, pp. 135–141.
Mathematical Reviews (MathSciNet): MR96e:35154
Zentralblatt MATH: 0850.35103
[13] S. P. Tsarev, Poisson brackets and one-dimensional Hamiltonian systems of hydrodynamic type, Soviet Math. Dokl 31 (1985), 488–491.
Zentralblatt MATH: 0605.35075
Mathematical Reviews (MathSciNet): MR796577
[14] S. Venakides, The zero dispersion limit of the Korteweg-de Vries equation for initial potentials with nontrivial reflection coefficient, Comm. Pure Appl. Math. 38 (1985), no. 2, 125–155.
Mathematical Reviews (MathSciNet): MR87d:35129
Zentralblatt MATH: 0571.35095
Digital Object Identifier: doi:10.1002/cpa.3160380202
[15] G. B. Whitham, Nonlinear dispersive waves, Proc. Roy. Soc. London Ser. A 139 (1965), 283–291.
[16] O. C. Wright, Korteweg-de Vries zero dispersion limit: through first breaking for cubic-like analytic initial data, Comm. Pure Appl. Math. 46 (1993), no. 3, 423–440.
Mathematical Reviews (MathSciNet): MR94d:35146
Zentralblatt MATH: 0789.35148
Digital Object Identifier: doi:10.1002/cpa.3160460306
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