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Generalizations of the Camassa-Holm equation. (English) Zbl 1181.37100
The author considers polynomial homogeneous generalizations of the Camassa-Holm type equation with quadratic and cubic nonlinearity and presented the corresponding Lax representations or linearization transformations for these equations. Some of the obtained equations seem to be new.

MSC:
37K10Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies
37K15Integration of completely integrable systems by inverse spectral and scattering methods
37K35Lie-Bäcklund and other transformations