title: Dispersive shock wave interactions and asymptotics.
abstract: Dispersive shock waves (DSWs) are physically important phenomena that occur in systems dominated by weak dispersion and weak nonlinearity. The Korteweg-de Vries (KdV) equation is the universal model for systems with weak dispersion and weak, quadratic nonlinearity. Here we show that the long-time-asymptotic solution of the KdV equation for general, steplike data is a single-phase DSW; this DSW is the "largest" possible DSW based on the boundary data. We find this asymptotic solution using the inverse scattering transform and matched-asymptotic expansions. So while multistep data evolve to have multiphase dynamics at intermediate times, these interacting DSWs eventually merge to form a single-phase DSW at large time.
authors.affiliation: Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309-0526, USA.
authors.forename: Mark J
authors.initials: MJ
authors.lastname: Ablowitz
authors.forename: Douglas E
authors.initials: DE
authors.lastname: Baldwin
mesh_terms: D003198:Computer Simulation; D004735:Energy Transfer; D008962:Models, Theoretical; D017711:Nonlinear Dynamics