The problem of scattering of particles on the line with repulsive interactions, gives rise to some well-known integrable Hamiltonian systems, for example, the nonperiodic Toda lattice or Calogero's system. The aim of this note is to outline our researches which proved the integrability of a much larger class of systems, including some that had never been considered, such as the scattering with very-long-range interaction potential. The integrability of all these systems survives any small enough perturbation of the potential in an arbitrary compact set. Our framework is based on the concept of cone potentials, as defined below, which include the scattering on the line as a particular case.
In Section 2 we present some remarkable examples that are covered by our theory. In Section 3 we discuss the related literature. Finally, in Section 4 we write down the statements of the results.of s much larger class of systems, including some thst had never been considered, such as the scattering with very-long-range interaction potentisl. The integrability of all these systems survives any small enough perturbation of the potential in sn arbitrsry compact set. Our framework is based on the concept of cone potentisls, as defined below, which include the scattering on the line as a particular case.
In Section 2 we present some remsrkable exsmples that sre covered by our theory. In Section 3 we discuss the related literature. Finally, in Section 4 we write down the statements of the results.
