| Abstract: |
| The standard AKNS scheme for generating integrable evolution systems is modified to obtain integrable peakon systems. In the simplest case of 2x2 matrices, the modified scheme yields two large families of integrable multi-component peakon equations, together with their recursion operators, symmetries, conservation laws, and bi-Hamiltonian structure. These families includes the well-known Camassa-Holm equation, the modified Camassa-Holm (FORQ) equation, their 2-component generalizations, Qiao`s equation involving arbitrary functions, and new peakon equations with nonlinearity coefficients that depend on the spatial variable x. |
|