Reutskiy, S.; Tirozzi, B. Forecast of the trajectory of the center of typhoons and the Maslov decomposition. (English) Zbl 1136.86004 Russ. J. Math. Phys. 14, No. 2, 232-237 (2007). Summary: We predict the trajectory of the center of a typhoon by using the coordinates of the first three positions of the center. From this information, we obtain the initial distribution of the wind velocity using a neural network trained for solving this inverse problem. We take the wind field at the initial time as the sum of a smooth part and a singular part, according to the Maslov theory. This form of the field ensures the stability and self-similarity of the flow. The trajectory is found by solving the shallow water equations numerically. In some cases, the resulting trajectory approximates the actual trajectory fairly well. Cited in 2 Documents MSC: 86A10 Meteorology and atmospheric physics 76B47 Vortex flows for incompressible inviscid fluids PDF BibTeX XML Cite \textit{S. Reutskiy} and \textit{B. Tirozzi}, Russ. J. Math. Phys. 14, No. 2, 232--237 (2007; Zbl 1136.86004) Full Text: DOI References: [1] Y. Wang, ”An Explicit Simulation of Tropical Cyclones with a Triply Nested Movable Mesh Primitive Equation Model: TMC3. Part I: Model Description and Control Experiment”, Mon. Wea. Rev. 129, 1370–1394 (2001). · doi:10.1175/1520-0493(2001)129<1370:AESOTC>2.0.CO;2 [2] V. G. Danilov, V. P. Maslov, and V. M. Shelkovich, ”Algebras of Singularities of Generalized Solutions of Strictly Hyperbolic Systems of Quasilinear First-Order Systems,” Teoret. Mat. Fiz. 114(1), 3–55 (1998). · Zbl 0946.35049 · doi:10.4213/tmf827 [3] S. Yu. Dobrokhotov, E. Semonov, B. Tirozzi, ”Hugoniot-Maslov Chains for Singular Vortex Solutions of Quasilinear Hyperbolic Systems and for a Typhoon Trajectory,” J. Math. Sci. 124(5), 5209–5249 (2004). · Zbl 1069.37049 · doi:10.1023/B:JOTH.0000047350.22539.ef [4] S. Dobrokhotov, A. I. Shafarevich, and B. Tirozzi, ”The Cauchy-Riemann Conditions and Localized Asymptotic Solutions of Linearized Equations in Shallow Water Theory,” Prikl. Mat. Mekh. 69(5), 804–809 (2005) [Appl. Math. Mech. 69 (5), 720–725 (2006)]. · Zbl 1100.76506 [5] S. Dobrokhotov, E. Semonov, and B. Tirozzi, ”Hugoniot-Maslov Chain for a System of Shallow-Water Equations Taking Energy Exchange into Account,” Mat. Zametki 78(5), 796–799 (2005) [Math. Notes 78 (5), 740–743 (2005)]. · doi:10.4213/mzm2643 [6] B. Tirozzi, S. Puca, S. Pittalis, A. Bruschi, S. Morucci, E. Ferraro, and S. Corsini, Neural Networks and Sea Time Series Reconstruction and Extreme-Event Analysis, MSSET (Birkhauser, Boston, 2005). · Zbl 1094.62121 [7] G. B. Whitham, Linear and Nonlinear Waves (Wiley Interscience, N.Y., 1974). [8] D. R. Durran, M. J. Yang, D. N. Slinn, and R. G. Brown, ”Toward More Accurate Wave-Permeable Boundary Conditions,” Mon. Wea. Rev. 121, 604–620 (1993). · doi:10.1175/1520-0493(1993)121<0604:TMAWPB>2.0.CO;2 [9] D. Givoli and B. Neta, ”High-Order Nonreflecting Boundary Conditions for the Dispersive Shallow Water Equations,” J. Comput. Appl. Math. 158(1), 49–60 · Zbl 1107.76377 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.