We extend Gérard’s formula for the solution of the Benjamin–Ono equation on the
line to square integrable and real valued initial data. Combined with this
formula, we also extend Gérard’s formula for the zero dispersion limit of the
Benjamin–Ono equation on the line to more singular initial data. In the
derivation of the extension of the formula for the zero dispersion limit, we
also find an interesting integral equality, which might be useful in other
contexts.
Keywords
Benjamin–Ono equation, explicit formula, zero dispersion
limit
