The Benjamin-Ono Initial-Value Problem for Rational Data - Centre Henri Lebesgue
Pré-Publication, Document De Travail Année : 2024

The Benjamin-Ono Initial-Value Problem for Rational Data

Résumé

We show that the initial-value problem for the Benjamin-Ono equation on R with L 2 (R) rational initial data with only simple poles can be solved in closed form via a determinant formula involving contour integrals. The dimension of the determinant depends on the number of simple poles of the rational initial data only and the matrix elements depend explicitly on the independent variables (t, x) and the dispersion coefficient ǫ. This allows for various interesting asymptotic limits to be resolved quite efficiently.

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Dates et versions

hal-04747842 , version 1 (22-10-2024)

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Elliot Blackstone, Louise Gassot, Patrick Gérard, Peter Miller. The Benjamin-Ono Initial-Value Problem for Rational Data. 2024. ⟨hal-04747842⟩
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