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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:
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
37K15 Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems
37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems
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