(m)KdV Solitons on the Background of Quasi-Periodic Finite-Gap Solutions

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(m)KdV Solitons on the Background of Quasi-Periodic Finite-Gap Solutions is written by Fritz Gesztesy and published by American Mathematical Soc.. It's available with International Standard Book Number or ISBN identification 0821804065 (ISBN 10) and 9780821804063 (ISBN 13).

In the introductory section, we review the formulation of the Korteweg-de Vries (KdV) equation and of the modified KdV (mKdV) equation as a compatibility condition for a Lax pair of linear operators. We then illustrate Miura's transformation, which maps solutions of the mKdV into solutions of the KdV. We then give a general overview of the concept of soliton solutions relative to general backgrounds, and of the single and double commutation methods. Finally, we present the main results of the article. To avoid the clutter of too many technical details, the paper is organized in four sections and five appendices.