One dimensional conservative surface dynamics with broken parity: Arrested collapse versus coarsening

• We explore a model of conservative surface dynamics with broken parity.
• Numerical studies reveal two qualitatively distinct long-time behaviors.
• One is an unusual traveling wave: a “train of kinks” with frozen-in disorder.
• Theoretical scaling analysis of kink formation accounts for many numerical findings.

The conserved Kuramoto–Sivashinsky (cKS) equation describes the coarsening of an unstable solid surface that conserves mass and that is parity symmetric. When parity is a broken symmetry, a nonlinear third-order spatial derivative term must in general be included in the equation of motion. We show that the effects of this term can be dramatic. Numerical integrations reveal that if its coefficient is sufficiently large, a nearly constant speed “train of kinks” develops and coarsening appears to cease. An individual kink exhibits scaling behavior as it grows deeper and narrower until the fourth-order cKS nonlinearity averts a finite-time singularity.