Superharmonic instability for regularized long-wave models*

Abstract We examine the spectral stability and instability of periodic traveling waves for regularized long-wave models. Examples include Boussinesq, Benney–Luke, Benjamin–Bona–Mahony equations. Of particular interest is a striking new phenomenon—spectrum off imaginary axis extending into infinity. The spectrum linearized operator generalized Korteweg–de Vries equation, instance, lies along outside bounded set. model, by contrast, can vary markedly with parameters waves. perform rigorous asymptotics short wavelength perturbations to establish conditions under which tends infinity or some curve whose real part nonzero. conduct numerical experiments corroborate our analytical findings.