On the integrable perturbations of the Camassa–Holm equation

Abstract

We present an investigation of the nonlinear partial differential equations (PDE) which are asymptotically representable as a linear combination of the equations from the Camassa–Holm hierarchy. For this purpose we use the infinitesimal transformations of dependent and independent variables of the original PDE. This approach is helpful for the analysis of the systems of the PDE which can be asymptotically represented as the evolution equations of polynomial structure.