An Extension of Nonlinear Evolution Equations of the K-dV (mK-dV) Type to Higher Orders

An extension of nonlinear evolution equations to higher orders is investigated. Included are (i) a higher order Sawada-Kotera equation which cannot be derived from the functional derivative of higher order conserved quantities of the Sawada-Kotera equation; (ii) N -soliton solution and the inverse scattering form for the higher order Sawada-Kotera equation; (iii) N -soliton solutions, the Backlund transformation and the inverse scattering form for higher order modified K-dV equations; (iv) a list of several bilinear equations some of which are conjectured to have 3-soliton solutions.

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