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Nonclassical Approximate Symmetries of Evolution Equations with a Small Parameter
Symmetry, integrability and geometry: methods and applications, Tome 2 (2006) Cet article a éte moissonné depuis la source Math-Net.Ru

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We introduce a method of approximate nonclassical Lie–Bäcklund symmetries for partial differential equations with a small parameter and discuss applications of this method to finding of approximate solutions both integrable and nonintegrable equations.
Keywords: nonclassical Lie–Bäcklund symmetries; approximate symmetry; conditional invariant solution. 
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     author = {Svetlana Kordyukova},
     title = {Nonclassical {Approximate} {Symmetries} of {Evolution} {Equations} with {a~Small} {Parameter}},
     journal = {Symmetry, integrability and geometry: methods and applications},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2006_2_a39/}
}
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Svetlana Kordyukova. Nonclassical Approximate Symmetries of Evolution Equations with a Small Parameter. Symmetry, integrability and geometry: methods and applications, Tome 2 (2006). http://geodesic.mathdoc.fr/item/SIGMA_2006_2_a39/

[1] J. Soviet Math., 55 (1991), 1450–1490 | DOI | MR | MR

[2] Bluman G. W., Cole J. D., “The general similarity solutions of the heat equation”, J. Math. Mech., 18 (1969), 1025–1042 | MR | Zbl

[3] Olver P. J., Rosenau P., “The construction of special solutions to partial differential equation”, Phys. Lett. A, 114 (1986), 107–112 | DOI | MR | Zbl

[4] Clarkson P. A., Kruskal M., “New similarity reductions of the Boussinesq equation”, J. Math. Phys., 30 (1989), 2201–2213 | DOI | MR | Zbl

[5] Kluwer, Dordrecht, 1993 | MR | Zbl

[6] Theor. Math. Phys., 99:2 (1994), 571–582 | DOI | MR | Zbl

[7] Zhdanov R. Z., “Conditional Lie–Bäcklund symmetry and reduction of evolution equations”, J. Phys. A: Math. Gen., 28 (1995), 3841–3850 | DOI | MR | Zbl

[8] Mahomed F. M., Qu C., “Approximate conditional symmetries for partial differential equations”, J. Phys. A: Math. Gen., 33 (2000), 343–356 | DOI | MR | Zbl

[9] Kara A. F., Mahomed F. M., Qu C., “Approximate potential symmetries for partial differential equations”, J. Phys. A: Math. Gen., 33 (2000), 6601–6613 | DOI | MR | Zbl

[10] Olver P. J., Vorob'ev E. M., “Nonclassical and conditional symmetries”, CRC Handbook of Lie Group Analysis of Differential Equations, Vol. 3, ed. N. H. Ibragimov, CRC Press, Boca Raton, Florida, 1996, 291–328

[11] Sokolov V. V., Shabat A. B., “Classification of integrable evolution equations”, Mathematical Physics Reviews, Vol. 4, Soviet Sci. Rev. Sect. C Math. Phys. Rev., 4, Harwood Academic Publ., Chur, 1984, 221–280 | MR

[12] Baikov V. A., Kordyukova S. A., “Approximate symmetries of the Boussinesq equation”, Quaest. Math., 26 (2003), 1–14 | MR | Zbl

[13] Anderson R. L., Baikov V. A., Gazizov R. K. et al., CRC Handbook of Lie Group Analysis of Differential Equation, Vol. 3, CRC Press, Boca Raton, Florida, 1996, Chapter 2 | Zbl