On the integrability of a class of nonlinear dispersive wave equations. (English) Zbl 1089.35522

Summary: We investigate the integrability of a class of \(1+1\)-dimensional models describing nonlinear dispersive waves in continuous media, e.g., cylindrical compressible hyperelastic rods, shallow water waves, etc. The only completely integrable cases coincide with the Camassa-Holm and Degasperis-Procesi equations.


35Q35 PDEs in connection with fluid mechanics
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
Full Text: DOI arXiv


[1] Degasperis A Procesi M Asymptotic Integrability, in Symmetry and Perturbation Theory, Editors: Degasperis A and Gaeta G, World Scientific, Singapore, 1999, 23–37
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.