Geodesic
Approximate symmetries
Sbornik. Mathematics, Tome 64 (1989) no. 2, pp. 427-441 Cet article a éte moissonné depuis la source Math-Net.Ru

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A theory, based on the new concept of an approximate group, is developed for approximate group analysis of differential equations with a small parameter. An approximate Lie theorem is proved that enables one to construct approximate symmetries that are stable under small perturbations of the differential equations. The use of the algorithm is illustrated in detail by examples: approximate symmetries of nonlinear wave equations are considered along with a broad class of evolution equations that includes the Korteweg–de Vries and Burgers–Korteweg–de Vries equations. Tables: 2. Bibliography: 4 titles. 
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     title = {Approximate symmetries},
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     volume = {64},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1989_64_2_a9/}
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V. A. Baikov; R. K. Gazizov; N. Kh. Ibragimov. Approximate symmetries. Sbornik. Mathematics, Tome 64 (1989) no. 2, pp. 427-441. http://geodesic.mathdoc.fr/item/SM_1989_64_2_a9/

[1] Lie S., Engel F., Teorie der Transformationsgruppen, Bd. 1–3, Jeubner, Leipzig, 1888, 1890, 1893

[2] Ovsyannikov L. V., Gruppovoi analiz differentsialnykh uravnenii, Nauka, M., 1978 | MR

[3] Ibragimov N. X., Gruppy preobrazovanii v matematicheskoi fizike, Nauka, M., 1983 | MR

[4] Ames W. F., Adams E., Lohner R. J., “Group properties of $u_{tt}=\bigl[f(u)u_x\bigr]_x$”, Int. J. Nonlinear Mechanics, 16:5/6 (1981), 439–447 | DOI | MR | Zbl