Direct Scattering for the Benjamin–Ono Equation with Rational Initial Data. Issue 1 (14th December 2015)

• Record Type: Journal Article
• Authors: Miller, Peter D.; Wetzel, Alfredo N.
• Other Names: Biondini G. guestEditor.; Fokas A.S. guestEditor.
• Is Part Of: Studies in applied mathematics. Volume 137:Issue 1(2016)
• Page Start: 53
• Page End: 69
• Publication Date: 2015-12-14
• Subjects: Mathematics -- Periodicals; Mathématiques -- Périodiques; Mathématique; Mathématique appliquée; Ressource Internet (Descripteur de forme); Périodique électronique (Descripteur de forme); 519
• DOI: 10.1111/sapm.12101
• Languages: English
• ISSNs: 0022-2526

Abstract

Abstract : We compute the scattering data of the Benjamin–Ono equation for arbitrary rational initial conditions with simple poles. Specifically, we obtain explicit formulas for the Jost solutions and eigenfunctions of the associated spectral problem, yielding an Evans function for the eigenvalues and formulas for the phase constants and reflection coefficient.