Shock waves in one-dimensional models with cubic nonlinearity (Q1330735)

Shock waves are described qualitatively for a class of one-dimensional models with cubic nonlinearity (of the type of the modified Korteweg-de Vries equation): \(u_ t-6u^ 2u_ x + \gamma u_{xxx} = \nu u_{xx}\). Both the integrable and the nonintegrable case are considered. The behavior of a shock wave in the limit \(t \to \infty\) is considered.