Fokas, A. S.; Liu, Q. M. Asymptotic integrability of water waves. (English) Zbl 0982.76511 Phys. Rev. Lett. 77, No. 12, 2347-2351 (1996). Summary: The asymptotic integrability of the idealized water waves is formally established. Namely, it is shown that in the small amplitude, long wave limit there exists an explicit transformation which maps these equations to a system of two integrable equations. It is also shown that the concepts of master symmetries and of bi-Hamiltonian structures can be used to obtain similar results for other physical systems. Cited in 40 Documents MSC: 76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction 37N10 Dynamical systems in fluid mechanics, oceanography and meteorology Keywords:asymptotic integrability; idealized water waves; small amplitude long wave limit; transformation; master symmetries; bi-Hamiltonian structures PDF BibTeX XML Cite \textit{A. S. Fokas} and \textit{Q. M. Liu}, Phys. Rev. Lett. 77, No. 12, 2347--2351 (1996; Zbl 0982.76511) Full Text: DOI References: [1] G. B. Whitham, in: Linear and Nonlinear Waves (1974) · Zbl 0373.76001 [2] C. S. Gardner, Phys. Rev. Lett. 19 pp 1095– (1967) · doi:10.1103/PhysRevLett.19.1095 [3] D. J. Korteweg, Philos. Mag. Ser. 5 pp 422– (1895) · doi:10.1080/14786449508620739 [4] Y. Kodama, Phys. Lett. 107A pp 245– (1985) · Zbl 1177.37058 · doi:10.1016/0375-9601(85)90207-5 [5] B. Fuchssteiner, Physica (Amsterdam) 4D pp 47– (1981) [6] B. Fuchssteiner, Prog. Theor. Phys. 65 pp 861– (1981) · Zbl 1074.58501 · doi:10.1143/PTP.65.861 [7] R. Camassa, Phys. Rev. Lett. 71 pp 1661– (1993) · Zbl 0972.35521 · doi:10.1103/PhysRevLett.71.1661 [8] A. S. Fokas, Acta Appl. Math. 39 pp 295– (1995) · Zbl 0842.58045 · doi:10.1007/BF00994638 [9] , Physica (Amsterdam) 87D pp 101– (1995) [10] Y. Kodama, Phys. Lett. 112A pp 193– (1985) · doi:10.1016/0375-9601(85)90500-6 [11] Y. Kodama, Phys. Lett. A 123 pp 276– (1987) · doi:10.1016/0375-9601(87)90227-1 [12] D. J. Kaup, Prog. Theor. Phys. 54 pp 396– (1975) · Zbl 1079.37514 · doi:10.1143/PTP.54.396 [13] A. S. Fokas, Phys. Lett. 86A pp 341– (1981) · doi:10.1016/0375-9601(81)90551-X This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.