Special solutions for an equation arising in sand ripple dynamics. (October 2022)

• Record Type: Journal Article
• Authors: Colucci, Renato
• Is Part Of: Nonlinear analysis. Volume 67(2022)
• Publication Date: 2022-10
• Subjects: Pattern formation -- Travelling wave solutions -- Sand ripples; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2022.103629
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We study a nonlinear fourth order evolution equation arising in the context of sand ripple dynamics. We analyse the set of stationary solutions and travelling waves in order to recover the observed phenomenology such as different wavelengths ripples, travelling waves, coarsening and time scales. Moreover, we construct an approximate solution which describes the early stages of the dynamics and which suggests the existence of coarsening and of time scales with different dynamical behaviour.