title: Nonlinear wave evolution equation for critical layers.
abstract: Recent studies of the evolution of weakly nonlinear long waves in shear flows have revealed that when the wave field contains a critical layer, a new nonlinear wave equation is needed to describe the wave evolution. This equation is of the same type as the well-known Korteweg-de Vries equation but has a more complicated nonlinear structure. Our main interest is in the steady solitary wave solutions when a nonlinear transformation converts the equation to a form equivalent to a steady Korteweg-de Vries equation. This enables the explicit construction of the steady solitary wave solutions.
authors.affiliation: Department of Mathematical Engineering, University of Concepción, Chile.
authors.forename: P
authors.initials: P
authors.lastname: Caillol
authors.forename: R
authors.initials: R
authors.lastname: Grimshaw