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Direct Scattering for the Benjamin–Ono Equation with Rational Initial Data
Author(s) -
Miller Peter D.,
Wetzel Alfredo N.
Publication year - 2016
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/sapm.12101
Subject(s) - eigenfunction , eigenvalues and eigenvectors , mathematical analysis , rational function , scattering , mathematics , simple (philosophy) , reflection (computer programming) , function (biology) , phase function , constant (computer programming) , scattering theory , phase (matter) , reflection coefficient , mathematical physics , physics , optics , quantum mechanics , computer science , philosophy , epistemology , evolutionary biology , biology , programming language
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.