Existence and Uniqueness of Solutions for a Quasilinear KdV Equation with Degenerate Dispersion. Issue 11 (8th May 2019) - Germain, Pierre; Harrop‐Griffiths, Benjamin; Marzuola, Jeremy L.
Abstract: We consider a quasilinear KdV equation that admits compactly supported traveling wave solutions (compactons). This model is one of the most straightforward instances of degenerate dispersion, a phenomenon that appears in a variety of physical settings as diverse as sedimentation, magma dynamics and shallow water waves. We prove the existence and uniqueness of solutions with sufficiently smooth, spatially localized initial data. © 2019 Wiley Periodicals, Inc.