Seminarium Nieliniowość i Geometria

A long-standing problem in the theory of Integrable Systems is how toconstruct new integrable systems. For systems in Classical Mechanics a veryproficient method was introduced by Ballesteros and Ragnisco in mid-90s. Such amethod is based on the notion of coalgebra, and roughly speaking allows theextension of integrable systems in one-degree of freedom to an arbitrary numberof degrees of freedom. In this talk I will review the fundamental ideas of thisapproach and present some novel applications also outside its originalformulation.Based on joint works with Danilo Latini, Benjamin K. Tapley, and Bert van Geemen