Deriving average soliton equations with a perturbative method

Ballantyne, Gary J.; Gough, P.T.; Taylor, D.P.

doi:10.1103/physreve.51.825

Cited by 4 publications

(1 citation statement)

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“…There have been quiet a few of powerful techniques for dealing with this kind of the perturbation (see [1] [2] [3] [4] [5] and references therein). Various perturbed cases of integrable equations have been considered, including the perturbed KdV and MKdV equations [3] [6] [7] , the perturbed nonlinear Schrödinger equation [8] [9] , the perturbed Burgers equation [10] and the perturbed Benjamin-Ono equation [11] etc. A detailed survey for this kind of perturbation theory based upon the inverse scattering transformation was provided by Kivshar and Malomed [12].…”

Section: Introductionmentioning

confidence: 99%

Integrable theory of the perturbation equations

Fuchssteiner

1996

Chaos, Solitons & Fractals

343

210

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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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