Integrable Theory of the Perturbation Equations

Details Integrable Theory of the Perturbation Equations Integrable Theory of the Perturbation Equations

1996-04-22

arxiv.org/abs/solv-int/9604004v1

Physics

High Energy Physics

High Energy Physics - Theory

27 pages, latex, to appear in Chaos, Soliton & Fractals

Scientific paper

An integrable theory is developed for the perturbation equations engendered from small disturbances of solutions. It includes various integrable properties of the perturbation equations: hereditary recursion operators, master symmetries, linear representations (Lax and zero curvature representations) and Hamiltonian structures etc. and provides us a method to generate 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.

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