Solitons and discrete eigenfunctions of the recursion operator of non-linear evolution equations. I. The Caudrey-Dodd-Gibbon-Sawada-Kotera equation

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Abstract
The solution of the third-order isospectral equation of the Caudrey-Dodd-Gibbon-Sawada-Kotera equation (CDGSKE) for soliton potential is obtained recursively from the Riccati equation derived by iterating once the auto-Backlund transformation. It is then shown that the discrete eigenfunctions of the sixth-order recursion operator for this equation can be written in terms of the solutions of the isospectral equation. The behaviour of the 1-soliton solution which has certain novel features is studied. A sine-Gordon-like equation resembling the double-sine-Gordon equation is derived from the CDGSKE.