Jean Gaston Darboux

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Darboux, Jean Gaston

 

Born Aug. 13, 1842, in Nîmes; died Feb. 23. 1917, in Paris. French mathematician. Member of the Paris Academy of Sciences (1884) and its permanent secretary from 1900. Corresponding member of the St. Petersburg Academy of Sciences (1895).

Darboux’s principal works are devoted to problems of differential geometry (the theory of surfaces and the theory of curvilinear coordinates): Lectures on the General Theory of Surfaces (vols. 1 -4, 1887–96) and Lectures on Orthogonal Systems and Curvilinear Coordinates (1898). His research on geometry led him to investigate various problems of integrating differential equations. Important among his works in other branches of mathematics are the memoirs on the theory of integration and the theory of analytic functions and also his research on the problem of the expansion of functions in orthogonal functions, especially in Jacobi polynomials. In mechanics, Darboux engaged in fruitful work on various problems of kinematics, equilibrium, and small fluctuations of a system of points.

REFERENCES

Liapunov, A. M. “Gaston Darbu.” Iz. AN, 1917. vol. 11, pp. 351–52.
Hilbert, D. “Gaston Darboux (1842–1917).” Acta mathematica, 1920, vol. 42, pp. 269–73.
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The book reviews recent findings on rogue waves and presents solutions to the rogue wave formation, using several methods: the Darboux and bilinear transformations, algebra-geometric reduction, and inverse scattering and similarity transformations.
Darboux F, Davy P, Gascuel-Odoux C, Fluang C (2002) Evolution of soil surface roughness and flowpath connectivity in overland flow experiments.
Taking account of third-order dispersion, self-steepening, and other nonlinear effects, by Darboux transformation [11] described the rogue waves and rational solutions of the Hirota equation in the following form:
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From a general point of view, the pioneer works of Chebyshev, Darboux, Markov, Christoffel, and Stieltjes were fundamental.
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Inverse problems and nonlinear evolution equations; solutions, Darboux matrices and Weyl-Titchmarsh functions.
On the structure of the set of solutions of the Darboux problem for hyperbolic equations.
Damos las gracias a JeanRene Darboux (Universite de Bretagne Occidentale, Brest) por la primera lamina delgada de un pilon (MDCS1) el 2001, a Michel Rossy (UMR 6249, Laboratoire de Chrono-Environnement, Besangon) por las cuatro laminas delgadas de las muestras de la Sierra de Collserola (R1, R2, C2 y C3) y Joan Aranda (IREC) y Joan Sune (IREC) por las cuatro laminas de la Roqueta y las dos de la Vall Salina.
Also he has studied Darboux frame and its derivative formulas for non-unit speed curves and surface pair in [E.