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Multiphase averaging and the inverse spectral solution of the Korteweg-de Vries equation. (English) Zbl 0454.35080

MSC:
35Q99 Partial differential equations of mathematical physics and other areas of application
35P99 Spectral theory and eigenvalue problems for partial differential equations
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[1] McKean, Invent. Math. 30 pp 217– (1975)
[2] Dubrovin, Uspekhi Mat. Nauk. 31 pp 55– (1976)
[3] Linear and Nonlinear Waves, Wiley-Interscience, New York, 1974.
[4] Manakov, Zh. Eksp. Teor. Fiz. 65 pp 1392– (1973)
[5] Sov. Phys. JETP 38 pp 693– (1974)
[6] Segur, J. Math. Phys. 12 pp 710– (1976)
[7] Ablowitz, Stud. Appl. Math. 49 pp 225– (1970) · Zbl 0203.41001 · doi:10.1002/sapm1970493225
[8] Ablowitz, Stud. Appl. Math. 51 pp 17– (1972) · Zbl 0261.76010 · doi:10.1002/sapm197251117
[9] On the averaged Lagrangian technique for nonlinear dispersive waves, Ph.D. thesis, California Institute of Technology, 1971.
[10] Whitham, Proc. Roy. Soc. Ser. A 283 pp 238– (1965)
[11] Miura, SIAM J. Appl. Math. 26 pp 376– (1974)
[12] Date, Prog. Theor. Phys. Supp. 59 pp 107– (1976)
[13] Flaschka, Prog. Theor. Phys. 55 pp 438– (1976)
[14] Hayes, Proc. Roy. Soc. London, Ser. A 332 pp 199– (1973)
[15] Gardner, Comm. Pure Appl. Math. 27 pp 97– (1974)
[16] and , Ergodic Problems of Classical Mechanics, W. A. Benjamin, New York, 1968, Appendix 2.
[17] Introduction to Riemann Surfaces, Addison Wesley Publishing Company, Reading, Mass. Ch. 10, 1957. · Zbl 0078.06602
[18] Ph.D dissertation, Clarkson College, 1974, unpublished.
[19] Scott, Proc. IEEE 61 pp 1443– (1973)
[20] and , Canonical variables for periodic Sine-Gordon equation and a method of averaging, LA-UR 78–3318, Report of Los Alamos Scientific Laboratory, 1978.
[21] Krichever, Funktsional’nyi Analiz i Ego Prilozheniya 11 pp 15– (1977)
[22] Functional Anal and Its Application 11 pp 12– (1978)
[23] Differential Forms with Application to the Physical Sciences, Academic Press, New York, 1963.
[24] and , Zero dispersion limit for the KdV equation, preprint, Courant Institute, 1979.
[25] Cherednik, Funkts. Anal. Prilozhen. 12 pp 45– (1978)
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