2021
DOI: 10.48550/arxiv.2112.08574
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Norming constants of embedded bound states and bounded positon solutions of the Korteweg-de Vries equation

Abstract: In the context of the full line Schrodinger equation, we revisit the binary Darboux transformation (double commutation method) which inserts or removes any number of positive eigenvalues embedded into the absolutely continuous spectrum without altering the rest of scattering data. We then show that embedded eigenvalues produce an additional explicit term in the KdV solution. This term looks similar to multi-soliton solution and describes waves traveling in the direction opposite to solitons. It also resembles … Show more

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