A note on the persistence of leading 𝑁-waves of tsunami

Kovalyov, M.

doi:10.1090/qam/1878256

A note on the persistence of leading $N$-waves of tsunami

Author: M. Kovalyov
Journal: Quart. Appl. Math. 60 (2002), 1-10
MSC: Primary 76B15; Secondary 86A05
DOI: https://doi.org/10.1090/qam/1878256
MathSciNet review: MR1878256
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We consider a new class of $N$-wave solutions for the KdV with the property that they periodically transform themselves from leading depression $N$-waves to leading elevation $N$-waves and back. We consider them as a possible model for the tsunami waves.

J. M. Abreu and Seabra Santos, Generation and propagation of tsunami produced by the movement of the ocean bed, Annales Geophysicae, Atmospheres, Hydrospheres and Space Sciences 10, No. 1–2 (1992)

M. J. Briggs and C. E. Synolakis, Large scale model tests of tsunami run-up, EOS, Wash. 73, 266 (1992)

M. J. Briggs, C. E. Synolakis, G. S. Harkin, and D. R. Green, Laboratory experiments of tsunami runup on a circular island, PAGEOPH 144, 3/4, 569–593 (1995)

G. F. Carrier, On-shelf generation and coastal propagation, Proc. IUGG/IOC Internat. Tsunami Sympos., Wakayama, Japan, 1993, pp. 23–40

G. F. Carrier and R. P. Shaw, Response of narrow-mouthed harbors to tsunami, Tsunami in The Pacific Ocean, East-West Center Press, Proceedings of the International Tsunami Symposium (1969)

V. Davletshin and D. D. Lappo, Tsunami forces exerted on vertical cylindrical barriers, Fluid Mechanics - Soviet Research, 15, No. 3 (1986)

Clifford S. Gardner, John M. Greene, Martin D. Kruskal, and Robert M. Miura, Korteweg-deVries equation and generalization. VI. Methods for exact solution, Comm. Pure Appl. Math. 27 (1974), 97–133. MR 336122, DOI https://doi.org/10.1002/cpa.3160270108

S. Ide, F. Imamura, Y. Yoshida, and K. Abe, Source characteristics of the Nicaraguan tsunami earthquake of September 2, 1992, Geophys. Res. Lett. 20, 863–866 (1993)

T. Iwasaki, Behaviour of tsunami waves, Navigation 83 (1985)

V. P. Koryavov, Electromagnetic fields associated with tsunami propagation, Izvestiya Academy of Sciences USSR, Physics of the Solid Earth 28, No. 2 (1992)

M. Kovalyov, Basic motions of the Korteweg-de Vries equation, Nonlinear Anal. 31 (1998), no. 5-6, 599–619. MR 1487849, DOI https://doi.org/10.1016/S0362-546X%2897%2900426-4
M. Kovalyov, Modulating properties of harmonic breather solutions of KdV, J. Phys. A 31 (1998), no. 22, 5117–5128. MR 1631440, DOI https://doi.org/10.1088/0305-4470/31/22/012
Mikhail Kovalyov, On the structure of the two-soliton interaction for the Korteweg-de Vries equation, J. Differential Equations 152 (1999), no. 2, 431–438. MR 1674573, DOI https://doi.org/10.1006/jdeq.1998.3537
Philip L.-F. Liu, Yong-Sik Cho, Michael J. Briggs, Utku Kanoglu, and Costas Emmanuel Synolakis, Runup of solitary waves on a circular island, J. Fluid Mech. 302 (1995), 259–285. MR 1360390, DOI https://doi.org/10.1017/S0022112095004095
Vladimir B. Matveev, Asymptotics of the multipositon-soliton $\tau $ function of the Korteweg-de Vries equation and the supertransparency, J. Math. Phys. 35 (1994), no. 6, 2955–2970. MR 1275482, DOI https://doi.org/10.1063/1.530496

R. Mazova and E. N. Pelinovskii, Linear theory of tsunami wave runup on a beach, Izvestiya Akademii Nauk SSSR, Fizika Atmosfery i Okeana 18, No. 2 (1982)

R. E. Meyer, On the shore singularity of water waves. I. The local model, Phys. Fluids 29 (1986), no. 10, 3152–3163. MR 861941, DOI https://doi.org/10.1063/1.865967
R. E. Meyer, On the shore singularity of water waves. I. The local model, Phys. Fluids 29 (1986), no. 10, 3152–3163. MR 861941, DOI https://doi.org/10.1063/1.865967

T. Nakayata, Boundary element analysis of non-linear water wave problems, International Journal for Numerical Methods in Engineering 19, No. 7 (1983)

S. Novikov, S. V. Manakov, L. P. Pitaevskiĭ, and V. E. Zakharov, Theory of solitons, Contemporary Soviet Mathematics, Consultants Bureau [Plenum], New York, 1984. The inverse scattering method; Translated from the Russian. MR 779467

Y. N. Pelinovski and T. G. Talipova, Height variations of large-amplitude solitary waves in the near-shore zone, Oceanology 17, No. 1 (1997)

K. Satake, J. Bourgeois, K. Abe, Y. Tsuji, F. Imamura, Y. Io, H. Katao, E. Noguera, and F. Estrada, Tsunami field survey of the 1992 Nicaragua Earthquake, EOS, Transactions, AGO 74, 145, 156 (1993)

C. E. Synolakis, Are solitary waves the limiting waves in the long wave run-up?, Proc. ASCE, 21st Conf. Coastal Engineering, Costa del Sol, Malaga, Spain, 1988, pp. 219–233

C. E. Synolakis, The run-up of solitary waves, Journal of Fluid Mechanics 185 (1987)

C. E. Synolakis, F. Imamura, Y. Tsuji, S. Matsutomi, B. Tinti, B. Cook, and M. Ushman, Damage, conditions of east Jave tsunami of 1994 analyzed, EOS, Transactions, American Geophysical Union 76 (26), 257 and 261–262 (1995)

S. Tadepalli and C. E. Synolakis, Model for the leading waves of tsunamis, Physical Review Letters 77, 2141–2144 (1996)

S. Tadepalli and C. E. Synolakis, The run-up of N-waves on sloping beaches, Proceedings of the Royal Society of London, Series A 445, 99–112 (1994)

G. B. Whitham, Linear and nonlinear waves, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1974. Pure and Applied Mathematics. MR 0483954

J. B. Williams and J. M. Jordan, A laboratory model of a doubled-humpted wave impingent on a plane, Sloping Beach. Tsunami in the Pacific Ocean, East-West Center Press, Proceedings of the International Symposium on Tsunami, 1969