Dispersive shock wave interactions and asymptotics

作者：Ablowitz Mark J^*; Baldwin Douglas E

来源：Physical Review E, 2013, 87(2): 022906.

DOI：10.1103/PhysRevE.87.022906

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. DOI: 10.1103/PhysRevE.87.022906

• 出版日期2013-2-13