Formation of compression waves with multiscale asymptotics in the Burgers and KdV models
arXiv:1505.00868
Abstract
The Cauchy problem for the Burgers equation with a small dissipation and an initial weak discontinuity and the Cauchy problem with a large initial gradient for a quasilinear parabolic equation and for the Korteweg-de Vries (KdV) equation are considered. Multiscale asymptotics of solutions corresponding to shock waves are constructed. Some results can also be applied to rarefaction waves.
Keywords: Burgers equation, KdV equation, Cauchy problem, multiscale asymptotics, weak discontinuity, shock waves, renormalization. 12 pages