For third order completely integrable equations in 1 + 1 dimensions canonical transformations which map (in the multi-soliton case) gradients of action variables to gradients of angle variables are constructed. Furthermore, this action-angle map is shown always to be an infinitesimal symmetry...

Given the Lie algebra Lfp of vector fields of a free particle then in a joint field of interacting particles an interacton is defined as a direct summand isomorphic to Lfp. For several soliton equations it is shown how interactons can be obtained from various methods of symmetry analysis and how...

Bäcklund transformations between all known completely integrable third-order differential equations in (1 + 1)-dimensions are established and the corresponding transformations formulas for their hereditary operators and Hamiltonian formulations are exhibited. Some of these Bäcklund...