On the integrable perturbations of the Camassa-Holm equation. (English) Zbl 1052.37058

Summary: The authors present an investigation of the nonlinear partial differential equations which are asymptotically representable as a linear combination of the equations from the Camassa-Holm hierarchy. For this purpose they 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.


37K55 Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems
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