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Zbl 1080.37578
Ma, W.X.; Fuchssteiner, B.
Integrable theory of the perturbation equations. (English)
[J] Chaos Solitons Fractals 7, No. 8, 1227-1250 (1996). ISSN 0960-0779

Summary: An integrable theory is developed for the perturbation equations engendered from small disturbances of solutions. It includes various integrable properties of the perturbation equations, such as hereditary recursion operators, master symmetries, linear representations (Lax and zero curvature representations) and Hamiltonian structures, and provides us with a method of generating hereditary operators, Hamiltonian operators and symplectic operators starting from the known ones. The resulting perturbation equations give rise to a sort of integrable coupling of soliton equations. Two examples (MKdV hierarchy and KP equation) are carefully carried out.

MSC 2000:: *37J35 Completely integrable systems, etc.
35Q53 KdV-like equations
37J40 Perturbations, etc.

Cited in: Zbl 1135.37332

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