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Bilinear forms and Bäcklund transformations of the perturbation systems. (English) Zbl 1171.37332
Summary: A class of bilinear forms and a class of Bäcklund transformations are presented for the perturbation systems generated from perturbations around solutions of a given system of integrable equations. The stability notion of bilinear structures is introduced to guarantee their hereditariness from the original system to their perturbation systems. Two special choices of the resulting bilinear forms and Bäcklund transformations are discussed. The Korteweg-de Vries equation is chosen as a model to illustrate the general idea.

37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems
Full Text: DOI
[1] Fuchssteiner, B., (), 125
[2] Ma, W.X.; Fuchssteiner, B., Chaos solitons fractals, 7, 1227, (1996)
[3] Ma, W.X., Methods appl. anal., 7, 21, (2000)
[4] Hirota, R., (), 157
[5] Strampp, W., J. math. phys., 35, 5850, (1994)
[6] Matveev, V.B.; Matveev, V.B., Phys. lett. A, Phys. lett. A, 166, 209, (1992)
[7] Ma, W.X., Phys. lett. A, 301, 35, (2002)
[8] Lakshmanan, M.; Tamizhmani, K.M., J. math. phys., 26, 1189, (1985)
[9] Drazin, P.G.; Johnson, R.S., Solitons: an introduction, (1989), Cambridge Univ. Press Cambridge, UK · Zbl 0661.35001
[10] Ma, W.X.; Fuchssteiner, B., Phys. lett. A, 213, 49, (1996) · Zbl 0863.35106
[11] Ma, W.X., J. math. phys., 43, 1408, (2002)
[12] Guo, F.K.; Zhang, Y.F., Chaos solitons fractals, 22, 1063, (2004)
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