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A rigidity result for the Holm–Staley<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e28" altimg="si6.svg"><mml:mi>b</mml:mi></mml:math>-family of equations with application to the asymptotic stability of the Degasperis–Procesi peakon

A rigidity result for the Holm–Staley<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e28" altimg="si6.svg"><mml:mi>b</mml:mi></mml:math>-family of equations with application to the asymptotic stability of the Degasperis–Procesi peakon