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

6533b82bfe1ef96bd128de8c

RESEARCH PRODUCT

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

Pierre Gaillard

subject

[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph][ MATH.MATH-MP ] Mathematics [math]/Mathematical Physics [math-ph][PHYS.MPHY] Physics [physics]/Mathematical Physics [math-ph]Mathematics::Spectral Theory theta functions KdV Nonlinear Sciences::Exactly Solvable and Integrable Systems [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]Riemann surfaces:solitons [ PHYS.MPHY ] Physics [physics]/Mathematical Physics [math-ph][MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph]Nonlinear Sciences::Pattern Formation and Solitons positons

description

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.

year	journal	country	edition	language
2010-02-18

https://hal.archives-ouvertes.fr/hal-00466159v2/file/posarXiv2.pdf

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