Geodesic
Calculation of Integrals of the Hugoniot–Maslov Chain for Singular Vortical Solutions of the Shallow-Water Equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 139 (2004) no. 1, pp. 62-76 Cet article a éte moissonné depuis la source Math-Net.Ru

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We discuss the problems of the Hugoniot–Maslov chain integrability for singular vortical solutions of the shallow-water equations on the $\beta$ plane. We show that the complex variables used to derive the chain automatically give most of the integrals of the complete and the truncated chains. We also study how some of these integrals are related to the Lagrangian invariant (potential vorticity). We discuss how to choose solutions of the chain that can be used to describe the actual trajectories of tropical cyclones.
Keywords: singular vortical solutions, trajectories, shallow water, integrals
Mots-clés : chains. 
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     title = {Calculation of {Integrals} of the {Hugoniot{\textendash}Maslov} {Chain} for {Singular} {Vortical} {Solutions} of the {Shallow-Water} {Equation}},
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S. Yu. Dobrokhotov; E. S. Semenov; B. Tirozzi. Calculation of Integrals of the Hugoniot–Maslov Chain for Singular Vortical Solutions of the Shallow-Water Equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 139 (2004) no. 1, pp. 62-76. http://geodesic.mathdoc.fr/item/TMF_2004_139_1_a4/

[1] V. P. Maslov, UMN, 35:2 (1980), 252–253

[2] V. G. Danilov, V. P. Maslov, V. M. Shelkovich, TMF, 114:1 (1998), 3–55 ; В. В. Булатов, Ю. В. Владимиров, В. Г. Данилов, С. Ю. Доброхотов, Докл. РАН, 338:1 (1994), 102–105 | DOI | MR | Zbl | MR | Zbl

[3] S. Yu. Dobrokhotov, Russ. J. Math. Phys., 6:2 (1999), 137–173 ; 3, 282–313 | MR | Zbl | MR | Zbl

[4] S. Yu. Dobrokhotov, TMF, 125:3 (2000), 491–517 | DOI | MR

[5] S. Yu. Dobrokhotov, K. V. Pankrashkin, E. S. Semenov, Russ. J. Math. Phys., 8:1 (2001), 25–54 | MR | Zbl

[6] E. S. Semenov, Matem. zametki, 71:6 (2002), 902–913 | DOI | MR | Zbl

[7] S. Yu. Dobrokhotov, B. Tirotstsi, Dokl. RAN, 384:6 (2002), 741–746 | MR | Zbl

[8] S. Yu. Dobrokhotov, E. S. Semenov, B. Tirozzi, “Hugóniot-Maslov chains for singular vortical solutions of quasi linear hyperbolic systems and typhoon trajectory”, Contemp. Math., 2004 (to appear) | MR | Zbl

[9] J. Pedlosky, Geophysical Fluid Dynamics, Springer, Berlin, 1982 ; Ф. В. Должанский, В. А. Крымов, Д. Ю. Манин, УФН, 160:7 (1990), 1–47 | DOI

[10] V. E. Zakharov, E. A. Kuznetsov, UFN, 167:11 (1997), 1137–1167 | DOI

[11] R. Ravindran, P. Prasad, Appl. Math. Lett., 3:2 (1990), 107–109 | DOI | MR

[12] V. F. Zaitsev, A. D. Polyanin, Spravochnik po obyknovennym differentsialnym uravneniyam, Fizmatlit, M., 1995 | MR

[13] C. Rogers, W. K. Schief, J. Math. Anal. Appl., 198:1 (1996), 194–220 ; C. Rogers, Phys. Lett. A, 138:6–7 (1989), 267–273 | DOI | MR | Zbl | DOI | MR