From finite-gap solutions of KdV in terms of theta functions to solitons and positons

Abstract : We degenerate the finite gap solutions of the KdV equation from the general formulation in terms of abelian functions when the gaps tends to points, to recover solutions of KdV equations in terms of wronskians called solitons or positons. For this we establish a link between Fredholm determinants and Wronskians.
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Pierre Gaillard. From finite-gap solutions of KdV in terms of theta functions to solitons and positons. 2010. ⟨hal-00466159v2⟩

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